The cohomology of $C_2$-equivariant Grassmannians $\text{Gr}_k(\mathbb{R}^{p,q})$ when $k=2$

$k=2$ $q=1$ $q=2$ $q=3$ $q=4$ $q=5$ $q=6$ $q$
$p=4$ $\text{Gr}_2(\mathbb{R}^{4,1})$ $\text{Gr}_2(\mathbb{R}^{4,2})$
$p=5$ $\text{Gr}_2(\mathbb{R}^{5,1})$ $\text{Gr}_2(\mathbb{R}^{5,2})$
$p=6$ $\text{Gr}_2(\mathbb{R}^{6,1})$ $\text{Gr}_2(\mathbb{R}^{6,2})$ $\text{Gr}_2(\mathbb{R}^{6,3})$
$p=7$ $\text{Gr}_2(\mathbb{R}^{7,1})$ $\text{Gr}_2(\mathbb{R}^{7,2})$ $\text{Gr}_2(\mathbb{R}^{7,3})$
$p=8$ $\text{Gr}_2(\mathbb{R}^{8,1})$ 2 possibilities $\text{Gr}_2(\mathbb{R}^{8,3})$ $\text{Gr}_2(\mathbb{R}^{8,4})$
$p=9$ $\text{Gr}_2(\mathbb{R}^{9,1})$ 4 possibilities 2 possibilities $\text{Gr}_2(\mathbb{R}^{9,4})$
$p=10$ $\text{Gr}_2(\mathbb{R}^{10,1})$ 8 possibilities 8 possibilities 2 possibilities $\text{Gr}_2(\mathbb{R}^{10,5})$
$p=11$ $\text{Gr}_2(\mathbb{R}^{11,1})$ 24 possibilities 48 possibilities 8 possibilities $\text{Gr}_2(\mathbb{R}^{11,5})$
$p=12$ $\text{Gr}_2(\mathbb{R}^{12,1})$ 72 possibilities 288 possibilities 96 possibilities 4 possibilities $\text{Gr}_2(\mathbb{R}^{12,6})$
$p=13$ $\text{Gr}_2(\mathbb{R}^{13,1})$ 216 possibilities ?? ?? ?? $\text{Gr}_2(\mathbb{R}^{13,6})$
$\quad\vdots$ $\quad\vdots$ $\quad\vdots$ $\quad\ddots$
$p$ $\text{Gr}_2(\mathbb{R}^{p,1})$ $\text{Gr}_2(\mathbb{R}^{p,2})$ $\text{Gr}_2(\mathbb{R}^{p,\left\lfloor\frac p2\right\rfloor})$

The cohomology of $\text{Gr}_2(\mathbb{R}^{4,1})$

Poincaré polynomial: $$x^{4} y^{2} + x^{3} y + 2 x^{2} y + x y + 1$$ Generator count grid:
1 1 2 2 1 1
Explicitly, as a free module over the ground ring $\mathbb{M}_2$: $$H^{\ast,\ast}(\text{Gr}_2(\mathbb{R}^{4,1}))=\mathbb{M}_2\oplus\Sigma^{1,1}\mathbb{M}_2\oplus\Sigma^{2,1}\mathbb{M}_2\oplus\Sigma^{3,1}\mathbb{M}_2\oplus\Sigma^{4,2}\mathbb{M}_2.$$




The cohomology of $\text{Gr}_2(\mathbb{R}^{4,2})$

Poincaré polynomial: $$x^{4} y^{2} + x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ Generator count grid:
1 1 1 1 1 1
Explicitly, as a free module over the ground ring $\mathbb{M}_2$: $$H^{\ast,\ast}(\text{Gr}_2(\mathbb{R}^{4,2}))=\mathbb{M}_2\oplus\Sigma^{1,1}\mathbb{M}_2\oplus\Sigma^{2,1}\mathbb{M}_2\oplus\Sigma^{2,2}\mathbb{M}_2\oplus\Sigma^{3,2}\mathbb{M}_2\oplus\Sigma^{4,2}\mathbb{M}_2.$$




The cohomology of $\text{Gr}_2(\mathbb{R}^{5,1})$

Poincaré polynomial: $$x^{6} y^{2} + x^{5} y^{2} + x^{4} y^{2} + x^{4} y + 2 x^{3} y + 2 x^{2} y + x y + 1$$ Generator count grid:
1 1 1 1 2 2 2 2 1 1
Explicitly, as a free module over the ground ring $\mathbb{M}_2$: $$H^{\ast,\ast}(\text{Gr}_2(\mathbb{R}^{5,1}))=\mathbb{M}_2\oplus\Sigma^{1,1}\mathbb{M}_2\oplus\Sigma^{2,1}\mathbb{M}_2\oplus\Sigma^{3,1}\mathbb{M}_2\oplus\Sigma^{4,1}\mathbb{M}_2\oplus\Sigma^{4,2}\mathbb{M}_2\oplus\Sigma^{5,2}\mathbb{M}_2\oplus\Sigma^{6,2}\mathbb{M}_2.$$




The cohomology of $\text{Gr}_2(\mathbb{R}^{5,2})$

Poincaré polynomial: $$x^{6} y^{3} + x^{5} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ Generator count grid:
1 1 2 2 2 2 1 1 1 1
Explicitly, as a free module over the ground ring $\mathbb{M}_2$: $$H^{\ast,\ast}(\text{Gr}_2(\mathbb{R}^{5,2}))=\mathbb{M}_2\oplus\Sigma^{1,1}\mathbb{M}_2\oplus\Sigma^{2,1}\mathbb{M}_2\oplus\Sigma^{2,2}\mathbb{M}_2\oplus\Sigma^{3,2}\mathbb{M}_2\oplus\Sigma^{4,2}\mathbb{M}_2\oplus\Sigma^{5,3}\mathbb{M}_2\oplus\Sigma^{6,3}\mathbb{M}_2.$$




The cohomology of $\text{Gr}_2(\mathbb{R}^{6,1})$

Poincaré polynomial: $$x^{8} y^{2} + x^{7} y^{2} + 2 x^{6} y^{2} + x^{5} y^{2} + x^{5} y + x^{4} y^{2} + 2 x^{4} y + 2 x^{3} y + 2 x^{2} y + x y + 1$$ Generator count grid:
1 1 2 2 1 1 1 2 2 2 2 2 2 1 1
Explicitly, as a free module over the ground ring $\mathbb{M}_2$: $$H^{\ast,\ast}(\text{Gr}_2(\mathbb{R}^{6,1}))=\mathbb{M}_2\oplus\Sigma^{1,1}\mathbb{M}_2\oplus\Sigma^{2,1}\mathbb{M}_2\oplus\Sigma^{3,1}\mathbb{M}_2\oplus\Sigma^{4,1}\mathbb{M}_2\oplus\Sigma^{4,2}\mathbb{M}_2\oplus\Sigma^{5,1}\mathbb{M}_2\oplus\Sigma^{5,2}\mathbb{M}_2\oplus\Sigma^{6,2}\mathbb{M}_2\oplus\Sigma^{7,2}\mathbb{M}_2\oplus\Sigma^{8,2}\mathbb{M}_2.$$




The cohomology of $\text{Gr}_2(\mathbb{R}^{6,2})$

Poincaré polynomial: $$x^{8} y^{4} + x^{7} y^{3} + 2 x^{6} y^{3} + x^{5} y^{3} + x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ Generator count grid:
1 1 2 2 1 1 3 3 3 2 2 1 1 1 1
Explicitly, as a free module over the ground ring $\mathbb{M}_2$: $$H^{\ast,\ast}(\text{Gr}_2(\mathbb{R}^{6,2}))=\mathbb{M}_2\oplus\Sigma^{1,1}\mathbb{M}_2\oplus\Sigma^{2,1}\mathbb{M}_2\oplus\Sigma^{2,2}\mathbb{M}_2\oplus\Sigma^{3,2}\mathbb{M}_2\oplus\Sigma^{4,2}\mathbb{M}_2\oplus\Sigma^{5,2}\mathbb{M}_2\oplus\Sigma^{5,3}\mathbb{M}_2\oplus\Sigma^{6,3}\mathbb{M}_2\oplus\Sigma^{7,3}\mathbb{M}_2\oplus\Sigma^{8,4}\mathbb{M}_2.$$




The cohomology of $\text{Gr}_2(\mathbb{R}^{6,3})$

Poincaré polynomial: $$x^{8} y^{4} + x^{7} y^{4} + x^{6} y^{4} + x^{6} y^{3} + 2 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ Generator count grid:
1 1 1 1 2 2 1 2 2 2 2 1 1 1 1
Explicitly, as a free module over the ground ring $\mathbb{M}_2$: $$H^{\ast,\ast}(\text{Gr}_2(\mathbb{R}^{6,3}))=\mathbb{M}_2\oplus\Sigma^{1,1}\mathbb{M}_2\oplus\Sigma^{2,1}\mathbb{M}_2\oplus\Sigma^{2,2}\mathbb{M}_2\oplus\Sigma^{3,2}\mathbb{M}_2\oplus\Sigma^{4,2}\mathbb{M}_2\oplus\Sigma^{4,3}\mathbb{M}_2\oplus\Sigma^{5,3}\mathbb{M}_2\oplus\Sigma^{6,3}\mathbb{M}_2\oplus\Sigma^{6,4}\mathbb{M}_2\oplus\Sigma^{7,4}\mathbb{M}_2\oplus\Sigma^{8,4}\mathbb{M}_2.$$




The cohomology of $\text{Gr}_2(\mathbb{R}^{7,1})$

Poincaré polynomial: $$x^{10} y^{2} + x^{9} y^{2} + 2 x^{8} y^{2} + 2 x^{7} y^{2} + 2 x^{6} y^{2} + x^{6} y + x^{5} y^{2} + 2 x^{5} y + x^{4} y^{2} + 2 x^{4} y + 2 x^{3} y + 2 x^{2} y + x y + 1$$ Generator count grid:
1 1 2 2 2 2 2 2 1 1 2 2 1 2 2 2 2 2 2 1 1
Explicitly, as a free module over the ground ring $\mathbb{M}_2$: $$H^{\ast,\ast}(\text{Gr}_2(\mathbb{R}^{7,1}))=\mathbb{M}_2\oplus\Sigma^{1,1}\mathbb{M}_2\oplus\Sigma^{2,1}\mathbb{M}_2\oplus\Sigma^{3,1}\mathbb{M}_2\oplus\Sigma^{4,1}\mathbb{M}_2\oplus\Sigma^{4,2}\mathbb{M}_2\oplus\Sigma^{5,1}\mathbb{M}_2\oplus\Sigma^{5,2}\mathbb{M}_2\oplus\Sigma^{6,1}\mathbb{M}_2\oplus\Sigma^{6,2}\mathbb{M}_2\oplus\Sigma^{7,2}\mathbb{M}_2\oplus\Sigma^{8,2}\mathbb{M}_2\oplus\Sigma^{9,2}\mathbb{M}_2\oplus\Sigma^{10,2}\mathbb{M}_2.$$




The cohomology of $\text{Gr}_2(\mathbb{R}^{7,2})$

Poincaré polynomial: $$x^{10} y^{4} + x^{9} y^{4} + x^{8} y^{4} + x^{8} y^{3} + 2 x^{7} y^{3} + 2 x^{6} y^{3} + x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ Generator count grid:
1 1 1 1 2 2 2 2 1 1 2 2 3 3 3 2 2 1 1 1 1
Explicitly, as a free module over the ground ring $\mathbb{M}_2$: $$H^{\ast,\ast}(\text{Gr}_2(\mathbb{R}^{7,2}))=\mathbb{M}_2\oplus\Sigma^{1,1}\mathbb{M}_2\oplus\Sigma^{2,1}\mathbb{M}_2\oplus\Sigma^{2,2}\mathbb{M}_2\oplus\Sigma^{3,2}\mathbb{M}_2\oplus\Sigma^{4,2}\mathbb{M}_2\oplus\Sigma^{5,2}\mathbb{M}_2\oplus\Sigma^{5,3}\mathbb{M}_2\oplus\Sigma^{6,2}\mathbb{M}_2\oplus\Sigma^{6,3}\mathbb{M}_2\oplus\Sigma^{7,3}\mathbb{M}_2\oplus\Sigma^{8,3}\mathbb{M}_2\oplus\Sigma^{8,4}\mathbb{M}_2\oplus\Sigma^{9,4}\mathbb{M}_2\oplus\Sigma^{10,4}\mathbb{M}_2.$$




The cohomology of $\text{Gr}_2(\mathbb{R}^{7,3})$

Poincaré polynomial: $$x^{10} y^{5} + x^{9} y^{5} + 2 x^{8} y^{4} + 2 x^{7} y^{4} + x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ Generator count grid:
1 1 2 2 2 2 1 2 2 3 3 3 1 2 2 2 2 1 1 1 1
Explicitly, as a free module over the ground ring $\mathbb{M}_2$: $$H^{\ast,\ast}(\text{Gr}_2(\mathbb{R}^{7,3}))=\mathbb{M}_2\oplus\Sigma^{1,1}\mathbb{M}_2\oplus\Sigma^{2,1}\mathbb{M}_2\oplus\Sigma^{2,2}\mathbb{M}_2\oplus\Sigma^{3,2}\mathbb{M}_2\oplus\Sigma^{4,2}\mathbb{M}_2\oplus\Sigma^{4,3}\mathbb{M}_2\oplus\Sigma^{5,3}\mathbb{M}_2\oplus\Sigma^{6,3}\mathbb{M}_2\oplus\Sigma^{6,4}\mathbb{M}_2\oplus\Sigma^{7,4}\mathbb{M}_2\oplus\Sigma^{8,4}\mathbb{M}_2\oplus\Sigma^{9,5}\mathbb{M}_2\oplus\Sigma^{10,5}\mathbb{M}_2.$$




The cohomology of $\text{Gr}_2(\mathbb{R}^{8,1})$

Poincaré polynomial: $$x^{12} y^{2} + x^{11} y^{2} + 2 x^{10} y^{2} + 2 x^{9} y^{2} + 3 x^{8} y^{2} + 2 x^{7} y^{2} + x^{7} y + 2 x^{6} y^{2} + 2 x^{6} y + x^{5} y^{2} + 2 x^{5} y + x^{4} y^{2} + 2 x^{4} y + 2 x^{3} y + 2 x^{2} y + x y + 1$$ Generator count grid:
1 1 2 2 2 2 3 3 3 2 2 1 2 2 2 2 1 2 2 1 2 2 2 2 2 2 1 1
Explicitly, as a free module over the ground ring $\mathbb{M}_2$: $$H^{\ast,\ast}(\text{Gr}_2(\mathbb{R}^{8,1}))=\mathbb{M}_2\oplus\Sigma^{1,1}\mathbb{M}_2\oplus\Sigma^{2,1}\mathbb{M}_2\oplus\Sigma^{3,1}\mathbb{M}_2\oplus\Sigma^{4,1}\mathbb{M}_2\oplus\Sigma^{4,2}\mathbb{M}_2\oplus\Sigma^{5,1}\mathbb{M}_2\oplus\Sigma^{5,2}\mathbb{M}_2\oplus\Sigma^{6,1}\mathbb{M}_2\oplus\Sigma^{6,2}\mathbb{M}_2\oplus\Sigma^{7,1}\mathbb{M}_2\oplus\Sigma^{7,2}\mathbb{M}_2\oplus\Sigma^{8,2}\mathbb{M}_2\oplus\Sigma^{9,2}\mathbb{M}_2\oplus\Sigma^{10,2}\mathbb{M}_2\oplus\Sigma^{11,2}\mathbb{M}_2\oplus\Sigma^{12,2}\mathbb{M}_2.$$




The AutoKron can't determine the cohomology of $\text{Gr}_2(\mathbb{R}^{8,2})$.

There are 2 possibilities.
Here are their Poincaré polynomials: $$x^{12} y^{4} + x^{11} y^{4} + 2 x^{10} y^{4} + x^{9} y^{4} + x^{9} y^{3} + x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{12} y^{4} + x^{11} y^{4} + 2 x^{10} y^{4} + x^{9} y^{4} + x^{9} y^{3} + 3 x^{8} y^{3} + 3 x^{7} y^{3} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ Here are the corresponding generator grids to these 2 possibilities:
1 1 2 2 1 1 1 2 2 2 2 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1





The cohomology of $\text{Gr}_2(\mathbb{R}^{8,3})$

Poincaré polynomial: $$x^{12} y^{6} + x^{11} y^{5} + 2 x^{10} y^{5} + x^{9} y^{5} + x^{9} y^{4} + 3 x^{8} y^{4} + 2 x^{7} y^{4} + x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ Generator count grid:
1 1 2 2 1 1 3 3 3 2 2 1 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
Explicitly, as a free module over the ground ring $\mathbb{M}_2$: $$H^{\ast,\ast}(\text{Gr}_2(\mathbb{R}^{8,3}))=\mathbb{M}_2\oplus\Sigma^{1,1}\mathbb{M}_2\oplus\Sigma^{2,1}\mathbb{M}_2\oplus\Sigma^{2,2}\mathbb{M}_2\oplus\Sigma^{3,2}\mathbb{M}_2\oplus\Sigma^{4,2}\mathbb{M}_2\oplus\Sigma^{4,3}\mathbb{M}_2\oplus\Sigma^{5,3}\mathbb{M}_2\oplus\Sigma^{6,3}\mathbb{M}_2\oplus\Sigma^{6,4}\mathbb{M}_2\oplus\Sigma^{7,3}\mathbb{M}_2\oplus\Sigma^{7,4}\mathbb{M}_2\oplus\Sigma^{8,4}\mathbb{M}_2\oplus\Sigma^{9,4}\mathbb{M}_2\oplus\Sigma^{9,5}\mathbb{M}_2\oplus\Sigma^{10,5}\mathbb{M}_2\oplus\Sigma^{11,5}\mathbb{M}_2\oplus\Sigma^{12,6}\mathbb{M}_2.$$




The cohomology of $\text{Gr}_2(\mathbb{R}^{8,4})$

Poincaré polynomial: $$x^{12} y^{6} + x^{11} y^{6} + x^{10} y^{6} + x^{10} y^{5} + 2 x^{9} y^{5} + x^{8} y^{5} + 2 x^{8} y^{4} + 3 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ Generator count grid:
1 1 1 1 2 2 1 2 2 3 3 3 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
Explicitly, as a free module over the ground ring $\mathbb{M}_2$: $$H^{\ast,\ast}(\text{Gr}_2(\mathbb{R}^{8,4}))=\mathbb{M}_2\oplus\Sigma^{1,1}\mathbb{M}_2\oplus\Sigma^{2,1}\mathbb{M}_2\oplus\Sigma^{2,2}\mathbb{M}_2\oplus\Sigma^{3,2}\mathbb{M}_2\oplus\Sigma^{4,2}\mathbb{M}_2\oplus\Sigma^{4,3}\mathbb{M}_2\oplus\Sigma^{5,3}\mathbb{M}_2\oplus\Sigma^{6,3}\mathbb{M}_2\oplus\Sigma^{6,4}\mathbb{M}_2\oplus\Sigma^{7,4}\mathbb{M}_2\oplus\Sigma^{8,4}\mathbb{M}_2\oplus\Sigma^{8,5}\mathbb{M}_2\oplus\Sigma^{9,5}\mathbb{M}_2\oplus\Sigma^{10,5}\mathbb{M}_2\oplus\Sigma^{10,6}\mathbb{M}_2\oplus\Sigma^{11,6}\mathbb{M}_2\oplus\Sigma^{12,6}\mathbb{M}_2.$$




The cohomology of $\text{Gr}_2(\mathbb{R}^{9,1})$

Poincaré polynomial: $$x^{14} y^{2} + x^{13} y^{2} + 2 x^{12} y^{2} + 2 x^{11} y^{2} + 3 x^{10} y^{2} + 3 x^{9} y^{2} + 3 x^{8} y^{2} + x^{8} y + 2 x^{7} y^{2} + 2 x^{7} y + 2 x^{6} y^{2} + 2 x^{6} y + x^{5} y^{2} + 2 x^{5} y + x^{4} y^{2} + 2 x^{4} y + 2 x^{3} y + 2 x^{2} y + x y + 1$$ Generator count grid:
1 1 2 2 2 2 3 3 3 3 3 3 3 3 3 1 2 2 2 2 2 2 2 2 1 2 2 1 2 2 2 2 2 2 1 1
Explicitly, as a free module over the ground ring $\mathbb{M}_2$: $$H^{\ast,\ast}(\text{Gr}_2(\mathbb{R}^{9,1}))=\mathbb{M}_2\oplus\Sigma^{1,1}\mathbb{M}_2\oplus\Sigma^{2,1}\mathbb{M}_2\oplus\Sigma^{3,1}\mathbb{M}_2\oplus\Sigma^{4,1}\mathbb{M}_2\oplus\Sigma^{4,2}\mathbb{M}_2\oplus\Sigma^{5,1}\mathbb{M}_2\oplus\Sigma^{5,2}\mathbb{M}_2\oplus\Sigma^{6,1}\mathbb{M}_2\oplus\Sigma^{6,2}\mathbb{M}_2\oplus\Sigma^{7,1}\mathbb{M}_2\oplus\Sigma^{7,2}\mathbb{M}_2\oplus\Sigma^{8,1}\mathbb{M}_2\oplus\Sigma^{8,2}\mathbb{M}_2\oplus\Sigma^{9,2}\mathbb{M}_2\oplus\Sigma^{10,2}\mathbb{M}_2\oplus\Sigma^{11,2}\mathbb{M}_2\oplus\Sigma^{12,2}\mathbb{M}_2\oplus\Sigma^{13,2}\mathbb{M}_2\oplus\Sigma^{14,2}\mathbb{M}_2.$$




The AutoKron can't determine the cohomology of $\text{Gr}_2(\mathbb{R}^{9,2})$.

There are 4 possibilities.
Here are their Poincaré polynomials: $$x^{14} y^{4} + x^{13} y^{4} + 2 x^{12} y^{4} + 2 x^{11} y^{4} + 2 x^{10} y^{4} + x^{10} y^{3} + x^{9} y^{4} + 2 x^{9} y^{3} + x^{8} y^{4} + 2 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{14} y^{4} + x^{13} y^{4} + 2 x^{12} y^{4} + 2 x^{11} y^{4} + 2 x^{10} y^{4} + x^{10} y^{3} + 3 x^{9} y^{3} + x^{8} y^{4} + 3 x^{8} y^{3} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{14} y^{4} + x^{13} y^{4} + 2 x^{12} y^{4} + 2 x^{11} y^{4} + 2 x^{10} y^{4} + x^{10} y^{3} + x^{9} y^{4} + 2 x^{9} y^{3} + 3 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{14} y^{4} + x^{13} y^{4} + 2 x^{12} y^{4} + 2 x^{11} y^{4} + 2 x^{10} y^{4} + x^{10} y^{3} + 3 x^{9} y^{3} + 4 x^{8} y^{3} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ Here are the corresponding generator grids to these 4 possibilities:
1 1 2 2 2 2 2 2 1 1 2 2 1 2 2 1 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 3 3 3 1 3 3 3 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 1 2 2 3 3 3 1 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 3 3 3 4 4 4 4 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1





The AutoKron can't determine the cohomology of $\text{Gr}_2(\mathbb{R}^{9,3})$.

There are 2 possibilities.
Here are their Poincaré polynomials: $$x^{14} y^{6} + x^{13} y^{6} + x^{12} y^{6} + x^{12} y^{5} + 2 x^{11} y^{5} + 2 x^{10} y^{5} + x^{10} y^{4} + x^{9} y^{5} + 2 x^{9} y^{4} + 3 x^{8} y^{4} + x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{14} y^{6} + x^{13} y^{6} + x^{12} y^{6} + x^{12} y^{5} + 2 x^{11} y^{5} + 2 x^{10} y^{5} + x^{10} y^{4} + 3 x^{9} y^{4} + 4 x^{8} y^{4} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ Here are the corresponding generator grids to these 2 possibilities:
1 1 1 1 2 2 2 2 1 1 2 2 3 3 3 1 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 1 1 2 2 2 2 1 3 3 3 4 4 4 4 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1





The cohomology of $\text{Gr}_2(\mathbb{R}^{9,4})$

Poincaré polynomial: $$x^{14} y^{7} + x^{13} y^{7} + 2 x^{12} y^{6} + 2 x^{11} y^{6} + x^{10} y^{6} + 2 x^{10} y^{5} + 3 x^{9} y^{5} + x^{8} y^{5} + 3 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ Generator count grid:
1 1 2 2 2 2 1 2 2 3 3 3 1 3 3 3 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
Explicitly, as a free module over the ground ring $\mathbb{M}_2$: $$H^{\ast,\ast}(\text{Gr}_2(\mathbb{R}^{9,4}))=\mathbb{M}_2\oplus\Sigma^{1,1}\mathbb{M}_2\oplus\Sigma^{2,1}\mathbb{M}_2\oplus\Sigma^{2,2}\mathbb{M}_2\oplus\Sigma^{3,2}\mathbb{M}_2\oplus\Sigma^{4,2}\mathbb{M}_2\oplus\Sigma^{4,3}\mathbb{M}_2\oplus\Sigma^{5,3}\mathbb{M}_2\oplus\Sigma^{6,3}\mathbb{M}_2\oplus\Sigma^{6,4}\mathbb{M}_2\oplus\Sigma^{7,4}\mathbb{M}_2\oplus\Sigma^{8,4}\mathbb{M}_2\oplus\Sigma^{8,5}\mathbb{M}_2\oplus\Sigma^{9,5}\mathbb{M}_2\oplus\Sigma^{10,5}\mathbb{M}_2\oplus\Sigma^{10,6}\mathbb{M}_2\oplus\Sigma^{11,6}\mathbb{M}_2\oplus\Sigma^{12,6}\mathbb{M}_2\oplus\Sigma^{13,7}\mathbb{M}_2\oplus\Sigma^{14,7}\mathbb{M}_2.$$




The cohomology of $\text{Gr}_2(\mathbb{R}^{10,1})$

Poincaré polynomial: $$x^{16} y^{2} + x^{15} y^{2} + 2 x^{14} y^{2} + 2 x^{13} y^{2} + 3 x^{12} y^{2} + 3 x^{11} y^{2} + 4 x^{10} y^{2} + 3 x^{9} y^{2} + x^{9} y + 3 x^{8} y^{2} + 2 x^{8} y + 2 x^{7} y^{2} + 2 x^{7} y + 2 x^{6} y^{2} + 2 x^{6} y + x^{5} y^{2} + 2 x^{5} y + x^{4} y^{2} + 2 x^{4} y + 2 x^{3} y + 2 x^{2} y + x y + 1$$ Generator count grid:
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 2 2 2 2 2 2 2 2 1 2 2 1 2 2 2 2 2 2 1 1
Explicitly, as a free module over the ground ring $\mathbb{M}_2$: $$H^{\ast,\ast}(\text{Gr}_2(\mathbb{R}^{10,1}))=\mathbb{M}_2\oplus\Sigma^{1,1}\mathbb{M}_2\oplus\Sigma^{2,1}\mathbb{M}_2\oplus\Sigma^{3,1}\mathbb{M}_2\oplus\Sigma^{4,1}\mathbb{M}_2\oplus\Sigma^{4,2}\mathbb{M}_2\oplus\Sigma^{5,1}\mathbb{M}_2\oplus\Sigma^{5,2}\mathbb{M}_2\oplus\Sigma^{6,1}\mathbb{M}_2\oplus\Sigma^{6,2}\mathbb{M}_2\oplus\Sigma^{7,1}\mathbb{M}_2\oplus\Sigma^{7,2}\mathbb{M}_2\oplus\Sigma^{8,1}\mathbb{M}_2\oplus\Sigma^{8,2}\mathbb{M}_2\oplus\Sigma^{9,1}\mathbb{M}_2\oplus\Sigma^{9,2}\mathbb{M}_2\oplus\Sigma^{10,2}\mathbb{M}_2\oplus\Sigma^{11,2}\mathbb{M}_2\oplus\Sigma^{12,2}\mathbb{M}_2\oplus\Sigma^{13,2}\mathbb{M}_2\oplus\Sigma^{14,2}\mathbb{M}_2\oplus\Sigma^{15,2}\mathbb{M}_2\oplus\Sigma^{16,2}\mathbb{M}_2.$$




The AutoKron can't determine the cohomology of $\text{Gr}_2(\mathbb{R}^{10,2})$.

There are 8 possibilities.
Here are their Poincaré polynomials: $$x^{16} y^{4} + x^{15} y^{4} + 2 x^{14} y^{4} + 2 x^{13} y^{4} + 3 x^{12} y^{4} + 2 x^{11} y^{4} + x^{11} y^{3} + 2 x^{10} y^{4} + 2 x^{10} y^{3} + x^{9} y^{4} + 2 x^{9} y^{3} + x^{8} y^{4} + x^{9} y^{2} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{16} y^{4} + x^{15} y^{4} + 2 x^{14} y^{4} + 2 x^{13} y^{4} + 3 x^{12} y^{4} + 2 x^{11} y^{4} + x^{11} y^{3} + x^{10} y^{4} + 3 x^{10} y^{3} + x^{9} y^{4} + 3 x^{9} y^{3} + x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{16} y^{4} + x^{15} y^{4} + 2 x^{14} y^{4} + 2 x^{13} y^{4} + 3 x^{12} y^{4} + 2 x^{11} y^{4} + x^{11} y^{3} + 2 x^{10} y^{4} + 2 x^{10} y^{3} + 3 x^{9} y^{3} + x^{8} y^{4} + x^{9} y^{2} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{16} y^{4} + x^{15} y^{4} + 2 x^{14} y^{4} + 2 x^{13} y^{4} + 3 x^{12} y^{4} + 2 x^{11} y^{4} + x^{11} y^{3} + x^{10} y^{4} + 3 x^{10} y^{3} + 4 x^{9} y^{3} + x^{8} y^{4} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{16} y^{4} + x^{15} y^{4} + 2 x^{14} y^{4} + 2 x^{13} y^{4} + 3 x^{12} y^{4} + 2 x^{11} y^{4} + x^{11} y^{3} + 2 x^{10} y^{4} + 2 x^{10} y^{3} + x^{9} y^{4} + 2 x^{9} y^{3} + x^{9} y^{2} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{16} y^{4} + x^{15} y^{4} + 2 x^{14} y^{4} + 2 x^{13} y^{4} + 3 x^{12} y^{4} + 2 x^{11} y^{4} + x^{11} y^{3} + x^{10} y^{4} + 3 x^{10} y^{3} + x^{9} y^{4} + 3 x^{9} y^{3} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{16} y^{4} + x^{15} y^{4} + 2 x^{14} y^{4} + 2 x^{13} y^{4} + 3 x^{12} y^{4} + 2 x^{11} y^{4} + x^{11} y^{3} + 2 x^{10} y^{4} + 2 x^{10} y^{3} + 3 x^{9} y^{3} + x^{9} y^{2} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{16} y^{4} + x^{15} y^{4} + 2 x^{14} y^{4} + 2 x^{13} y^{4} + 3 x^{12} y^{4} + 2 x^{11} y^{4} + x^{11} y^{3} + x^{10} y^{4} + 3 x^{10} y^{3} + 4 x^{9} y^{3} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ Here are the corresponding generator grids to these 8 possibilities:
1 1 2 2 2 2 3 3 3 2 2 1 2 2 2 2 1 2 2 1 1 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 2 2 1 1 3 3 3 1 3 3 3 1 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 2 2 1 2 2 2 2 3 3 3 1 1 3 3 3 1 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 2 2 1 1 3 3 3 4 4 4 4 1 3 3 3 1 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 2 2 1 2 2 2 2 1 2 2 1 3 3 3 2 2 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 2 2 1 1 3 3 3 1 3 3 3 3 3 3 2 2 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 2 2 1 2 2 2 2 3 3 3 1 4 4 4 4 1 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 2 2 1 1 3 3 3 4 4 4 4 4 4 4 4 1 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1





The AutoKron can't determine the cohomology of $\text{Gr}_2(\mathbb{R}^{10,3})$.

There are 8 possibilities.
Here are their Poincaré polynomials: $$x^{16} y^{6} + x^{15} y^{6} + 2 x^{14} y^{6} + x^{13} y^{6} + x^{13} y^{5} + x^{12} y^{6} + 2 x^{12} y^{5} + 2 x^{11} y^{5} + x^{11} y^{4} + 2 x^{10} y^{5} + 2 x^{10} y^{4} + x^{9} y^{5} + 2 x^{9} y^{4} + x^{9} y^{3} + 3 x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{16} y^{6} + x^{15} y^{6} + 2 x^{14} y^{6} + x^{13} y^{6} + x^{13} y^{5} + 3 x^{12} y^{5} + 3 x^{11} y^{5} + 2 x^{10} y^{5} + 2 x^{10} y^{4} + x^{9} y^{5} + 2 x^{9} y^{4} + x^{9} y^{3} + 3 x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{16} y^{6} + x^{15} y^{6} + 2 x^{14} y^{6} + x^{13} y^{6} + x^{13} y^{5} + x^{12} y^{6} + 2 x^{12} y^{5} + 2 x^{11} y^{5} + x^{11} y^{4} + x^{10} y^{5} + 3 x^{10} y^{4} + x^{9} y^{5} + 3 x^{9} y^{4} + 3 x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{16} y^{6} + x^{15} y^{6} + 2 x^{14} y^{6} + x^{13} y^{6} + x^{13} y^{5} + 3 x^{12} y^{5} + 3 x^{11} y^{5} + x^{10} y^{5} + 3 x^{10} y^{4} + x^{9} y^{5} + 3 x^{9} y^{4} + 3 x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{16} y^{6} + x^{15} y^{6} + 2 x^{14} y^{6} + x^{13} y^{6} + x^{13} y^{5} + x^{12} y^{6} + 2 x^{12} y^{5} + 2 x^{11} y^{5} + x^{11} y^{4} + 2 x^{10} y^{5} + 2 x^{10} y^{4} + 3 x^{9} y^{4} + x^{9} y^{3} + 4 x^{8} y^{4} + x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{16} y^{6} + x^{15} y^{6} + 2 x^{14} y^{6} + x^{13} y^{6} + x^{13} y^{5} + 3 x^{12} y^{5} + 3 x^{11} y^{5} + 2 x^{10} y^{5} + 2 x^{10} y^{4} + 3 x^{9} y^{4} + x^{9} y^{3} + 4 x^{8} y^{4} + x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{16} y^{6} + x^{15} y^{6} + 2 x^{14} y^{6} + x^{13} y^{6} + x^{13} y^{5} + x^{12} y^{6} + 2 x^{12} y^{5} + 2 x^{11} y^{5} + x^{11} y^{4} + x^{10} y^{5} + 3 x^{10} y^{4} + 4 x^{9} y^{4} + 4 x^{8} y^{4} + x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{16} y^{6} + x^{15} y^{6} + 2 x^{14} y^{6} + x^{13} y^{6} + x^{13} y^{5} + 3 x^{12} y^{5} + 3 x^{11} y^{5} + x^{10} y^{5} + 3 x^{10} y^{4} + 4 x^{9} y^{4} + 4 x^{8} y^{4} + x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ Here are the corresponding generator grids to these 8 possibilities:
1 1 2 2 1 1 1 2 2 2 2 1 2 2 2 2 1 2 2 1 3 3 3 2 2 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 2 2 2 2 1 2 2 1 3 3 3 2 2 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 1 3 3 3 1 3 3 3 3 3 3 2 2 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 1 3 3 3 1 3 3 3 3 3 3 2 2 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 2 2 2 2 3 3 3 1 4 4 4 4 1 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 2 2 2 2 3 3 3 1 4 4 4 4 1 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 1 3 3 3 4 4 4 4 4 4 4 4 1 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 1 3 3 3 4 4 4 4 4 4 4 4 1 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1





The AutoKron can't determine the cohomology of $\text{Gr}_2(\mathbb{R}^{10,4})$.

There are 2 possibilities.
Here are their Poincaré polynomials: $$x^{16} y^{8} + x^{15} y^{7} + 2 x^{14} y^{7} + x^{13} y^{7} + x^{13} y^{6} + 3 x^{12} y^{6} + 2 x^{11} y^{6} + x^{11} y^{5} + x^{10} y^{6} + 3 x^{10} y^{5} + 3 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{16} y^{8} + x^{15} y^{7} + 2 x^{14} y^{7} + x^{13} y^{7} + x^{13} y^{6} + 3 x^{12} y^{6} + 2 x^{11} y^{6} + x^{11} y^{5} + 4 x^{10} y^{5} + 4 x^{9} y^{5} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ Here are the corresponding generator grids to these 2 possibilities:
1 1 2 2 1 1 3 3 3 2 2 1 1 3 3 3 3 3 3 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 2 2 1 4 4 4 4 4 4 4 4 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1





The cohomology of $\text{Gr}_2(\mathbb{R}^{10,5})$

Poincaré polynomial: $$x^{16} y^{8} + x^{15} y^{8} + x^{14} y^{8} + x^{14} y^{7} + 2 x^{13} y^{7} + x^{12} y^{7} + 2 x^{12} y^{6} + 3 x^{11} y^{6} + 2 x^{10} y^{6} + 2 x^{10} y^{5} + 4 x^{9} y^{5} + 2 x^{8} y^{5} + 3 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ Generator count grid:
1 1 1 1 2 2 1 2 2 3 3 3 2 2 2 2 4 4 4 4 2 2 3 3 3 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
Explicitly, as a free module over the ground ring $\mathbb{M}_2$: $$H^{\ast,\ast}(\text{Gr}_2(\mathbb{R}^{10,5}))=\mathbb{M}_2\oplus\Sigma^{1,1}\mathbb{M}_2\oplus\Sigma^{2,1}\mathbb{M}_2\oplus\Sigma^{2,2}\mathbb{M}_2\oplus\Sigma^{3,2}\mathbb{M}_2\oplus\Sigma^{4,2}\mathbb{M}_2\oplus\Sigma^{4,3}\mathbb{M}_2\oplus\Sigma^{5,3}\mathbb{M}_2\oplus\Sigma^{6,3}\mathbb{M}_2\oplus\Sigma^{6,4}\mathbb{M}_2\oplus\Sigma^{7,4}\mathbb{M}_2\oplus\Sigma^{8,4}\mathbb{M}_2\oplus\Sigma^{8,5}\mathbb{M}_2\oplus\Sigma^{9,5}\mathbb{M}_2\oplus\Sigma^{10,5}\mathbb{M}_2\oplus\Sigma^{10,6}\mathbb{M}_2\oplus\Sigma^{11,6}\mathbb{M}_2\oplus\Sigma^{12,6}\mathbb{M}_2\oplus\Sigma^{12,7}\mathbb{M}_2\oplus\Sigma^{13,7}\mathbb{M}_2\oplus\Sigma^{14,7}\mathbb{M}_2\oplus\Sigma^{14,8}\mathbb{M}_2\oplus\Sigma^{15,8}\mathbb{M}_2\oplus\Sigma^{16,8}\mathbb{M}_2.$$




The cohomology of $\text{Gr}_2(\mathbb{R}^{11,1})$

Poincaré polynomial: $$x^{18} y^{2} + x^{17} y^{2} + 2 x^{16} y^{2} + 2 x^{15} y^{2} + 3 x^{14} y^{2} + 3 x^{13} y^{2} + 4 x^{12} y^{2} + 4 x^{11} y^{2} + 4 x^{10} y^{2} + x^{10} y + 3 x^{9} y^{2} + 2 x^{9} y + 3 x^{8} y^{2} + 2 x^{8} y + 2 x^{7} y^{2} + 2 x^{7} y + 2 x^{6} y^{2} + 2 x^{6} y + x^{5} y^{2} + 2 x^{5} y + x^{4} y^{2} + 2 x^{4} y + 2 x^{3} y + 2 x^{2} y + x y + 1$$ Generator count grid:
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 1 3 3 3 2 2 3 3 3 2 2 2 2 2 2 2 2 2 2 1 2 2 1 2 2 2 2 2 2 1 1
Explicitly, as a free module over the ground ring $\mathbb{M}_2$: $$H^{\ast,\ast}(\text{Gr}_2(\mathbb{R}^{11,1}))=\mathbb{M}_2\oplus\Sigma^{1,1}\mathbb{M}_2\oplus\Sigma^{2,1}\mathbb{M}_2\oplus\Sigma^{3,1}\mathbb{M}_2\oplus\Sigma^{4,1}\mathbb{M}_2\oplus\Sigma^{4,2}\mathbb{M}_2\oplus\Sigma^{5,1}\mathbb{M}_2\oplus\Sigma^{5,2}\mathbb{M}_2\oplus\Sigma^{6,1}\mathbb{M}_2\oplus\Sigma^{6,2}\mathbb{M}_2\oplus\Sigma^{7,1}\mathbb{M}_2\oplus\Sigma^{7,2}\mathbb{M}_2\oplus\Sigma^{8,1}\mathbb{M}_2\oplus\Sigma^{8,2}\mathbb{M}_2\oplus\Sigma^{9,1}\mathbb{M}_2\oplus\Sigma^{9,2}\mathbb{M}_2\oplus\Sigma^{10,1}\mathbb{M}_2\oplus\Sigma^{10,2}\mathbb{M}_2\oplus\Sigma^{11,2}\mathbb{M}_2\oplus\Sigma^{12,2}\mathbb{M}_2\oplus\Sigma^{13,2}\mathbb{M}_2\oplus\Sigma^{14,2}\mathbb{M}_2\oplus\Sigma^{15,2}\mathbb{M}_2\oplus\Sigma^{16,2}\mathbb{M}_2\oplus\Sigma^{17,2}\mathbb{M}_2\oplus\Sigma^{18,2}\mathbb{M}_2.$$




The AutoKron can't determine the cohomology of $\text{Gr}_2(\mathbb{R}^{11,2})$.

There are 24 possibilities.
Here are their Poincaré polynomials: $$x^{18} y^{4} + x^{17} y^{4} + 2 x^{16} y^{4} + 2 x^{15} y^{4} + 3 x^{14} y^{4} + 3 x^{13} y^{4} + 3 x^{12} y^{4} + x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + 2 x^{10} y^{4} + 2 x^{10} y^{3} + x^{9} y^{4} + x^{10} y^{2} + 2 x^{9} y^{3} + x^{8} y^{4} + 2 x^{9} y^{2} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{4} + x^{17} y^{4} + 2 x^{16} y^{4} + 2 x^{15} y^{4} + 3 x^{14} y^{4} + 3 x^{13} y^{4} + 3 x^{12} y^{4} + x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + 2 x^{10} y^{4} + 3 x^{10} y^{3} + x^{9} y^{4} + 2 x^{9} y^{3} + x^{8} y^{4} + 2 x^{9} y^{2} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{4} + x^{17} y^{4} + 2 x^{16} y^{4} + 2 x^{15} y^{4} + 3 x^{14} y^{4} + 3 x^{13} y^{4} + 3 x^{12} y^{4} + x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + x^{10} y^{4} + 3 x^{10} y^{3} + x^{9} y^{4} + x^{10} y^{2} + 3 x^{9} y^{3} + x^{8} y^{4} + x^{9} y^{2} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{4} + x^{17} y^{4} + 2 x^{16} y^{4} + 2 x^{15} y^{4} + 3 x^{14} y^{4} + 3 x^{13} y^{4} + 3 x^{12} y^{4} + x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + x^{10} y^{4} + 4 x^{10} y^{3} + x^{9} y^{4} + 3 x^{9} y^{3} + x^{8} y^{4} + x^{9} y^{2} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{4} + x^{17} y^{4} + 2 x^{16} y^{4} + 2 x^{15} y^{4} + 3 x^{14} y^{4} + 3 x^{13} y^{4} + 3 x^{12} y^{4} + x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + 4 x^{10} y^{3} + x^{9} y^{4} + x^{10} y^{2} + 4 x^{9} y^{3} + x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{4} + x^{17} y^{4} + 2 x^{16} y^{4} + 2 x^{15} y^{4} + 3 x^{14} y^{4} + 3 x^{13} y^{4} + 3 x^{12} y^{4} + x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + 5 x^{10} y^{3} + x^{9} y^{4} + 4 x^{9} y^{3} + x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{4} + x^{17} y^{4} + 2 x^{16} y^{4} + 2 x^{15} y^{4} + 3 x^{14} y^{4} + 3 x^{13} y^{4} + 3 x^{12} y^{4} + x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + 2 x^{10} y^{4} + 2 x^{10} y^{3} + x^{10} y^{2} + 3 x^{9} y^{3} + x^{8} y^{4} + 2 x^{9} y^{2} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{4} + x^{17} y^{4} + 2 x^{16} y^{4} + 2 x^{15} y^{4} + 3 x^{14} y^{4} + 3 x^{13} y^{4} + 3 x^{12} y^{4} + x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + 2 x^{10} y^{4} + 3 x^{10} y^{3} + 3 x^{9} y^{3} + x^{8} y^{4} + 2 x^{9} y^{2} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{4} + x^{17} y^{4} + 2 x^{16} y^{4} + 2 x^{15} y^{4} + 3 x^{14} y^{4} + 3 x^{13} y^{4} + 3 x^{12} y^{4} + x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + x^{10} y^{4} + 3 x^{10} y^{3} + x^{10} y^{2} + 4 x^{9} y^{3} + x^{8} y^{4} + x^{9} y^{2} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{4} + x^{17} y^{4} + 2 x^{16} y^{4} + 2 x^{15} y^{4} + 3 x^{14} y^{4} + 3 x^{13} y^{4} + 3 x^{12} y^{4} + x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + x^{10} y^{4} + 4 x^{10} y^{3} + 4 x^{9} y^{3} + x^{8} y^{4} + x^{9} y^{2} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{4} + x^{17} y^{4} + 2 x^{16} y^{4} + 2 x^{15} y^{4} + 3 x^{14} y^{4} + 3 x^{13} y^{4} + 3 x^{12} y^{4} + x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + 4 x^{10} y^{3} + x^{10} y^{2} + 5 x^{9} y^{3} + x^{8} y^{4} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{4} + x^{17} y^{4} + 2 x^{16} y^{4} + 2 x^{15} y^{4} + 3 x^{14} y^{4} + 3 x^{13} y^{4} + 3 x^{12} y^{4} + x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + 5 x^{10} y^{3} + 5 x^{9} y^{3} + x^{8} y^{4} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{4} + x^{17} y^{4} + 2 x^{16} y^{4} + 2 x^{15} y^{4} + 3 x^{14} y^{4} + 3 x^{13} y^{4} + 3 x^{12} y^{4} + x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + 2 x^{10} y^{4} + 2 x^{10} y^{3} + x^{9} y^{4} + x^{10} y^{2} + 2 x^{9} y^{3} + 2 x^{9} y^{2} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{4} + x^{17} y^{4} + 2 x^{16} y^{4} + 2 x^{15} y^{4} + 3 x^{14} y^{4} + 3 x^{13} y^{4} + 3 x^{12} y^{4} + x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + 2 x^{10} y^{4} + 3 x^{10} y^{3} + x^{9} y^{4} + 2 x^{9} y^{3} + 2 x^{9} y^{2} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{4} + x^{17} y^{4} + 2 x^{16} y^{4} + 2 x^{15} y^{4} + 3 x^{14} y^{4} + 3 x^{13} y^{4} + 3 x^{12} y^{4} + x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + x^{10} y^{4} + 3 x^{10} y^{3} + x^{9} y^{4} + x^{10} y^{2} + 3 x^{9} y^{3} + x^{9} y^{2} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{4} + x^{17} y^{4} + 2 x^{16} y^{4} + 2 x^{15} y^{4} + 3 x^{14} y^{4} + 3 x^{13} y^{4} + 3 x^{12} y^{4} + x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + x^{10} y^{4} + 4 x^{10} y^{3} + x^{9} y^{4} + 3 x^{9} y^{3} + x^{9} y^{2} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{4} + x^{17} y^{4} + 2 x^{16} y^{4} + 2 x^{15} y^{4} + 3 x^{14} y^{4} + 3 x^{13} y^{4} + 3 x^{12} y^{4} + x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + 4 x^{10} y^{3} + x^{9} y^{4} + x^{10} y^{2} + 4 x^{9} y^{3} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{4} + x^{17} y^{4} + 2 x^{16} y^{4} + 2 x^{15} y^{4} + 3 x^{14} y^{4} + 3 x^{13} y^{4} + 3 x^{12} y^{4} + x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + 5 x^{10} y^{3} + x^{9} y^{4} + 4 x^{9} y^{3} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{4} + x^{17} y^{4} + 2 x^{16} y^{4} + 2 x^{15} y^{4} + 3 x^{14} y^{4} + 3 x^{13} y^{4} + 3 x^{12} y^{4} + x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + 2 x^{10} y^{4} + 2 x^{10} y^{3} + x^{10} y^{2} + 3 x^{9} y^{3} + 2 x^{9} y^{2} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{4} + x^{17} y^{4} + 2 x^{16} y^{4} + 2 x^{15} y^{4} + 3 x^{14} y^{4} + 3 x^{13} y^{4} + 3 x^{12} y^{4} + x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + 2 x^{10} y^{4} + 3 x^{10} y^{3} + 3 x^{9} y^{3} + 2 x^{9} y^{2} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{4} + x^{17} y^{4} + 2 x^{16} y^{4} + 2 x^{15} y^{4} + 3 x^{14} y^{4} + 3 x^{13} y^{4} + 3 x^{12} y^{4} + x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + x^{10} y^{4} + 3 x^{10} y^{3} + x^{10} y^{2} + 4 x^{9} y^{3} + x^{9} y^{2} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{4} + x^{17} y^{4} + 2 x^{16} y^{4} + 2 x^{15} y^{4} + 3 x^{14} y^{4} + 3 x^{13} y^{4} + 3 x^{12} y^{4} + x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + x^{10} y^{4} + 4 x^{10} y^{3} + 4 x^{9} y^{3} + x^{9} y^{2} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{4} + x^{17} y^{4} + 2 x^{16} y^{4} + 2 x^{15} y^{4} + 3 x^{14} y^{4} + 3 x^{13} y^{4} + 3 x^{12} y^{4} + x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + 4 x^{10} y^{3} + x^{10} y^{2} + 5 x^{9} y^{3} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{4} + x^{17} y^{4} + 2 x^{16} y^{4} + 2 x^{15} y^{4} + 3 x^{14} y^{4} + 3 x^{13} y^{4} + 3 x^{12} y^{4} + x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + 5 x^{10} y^{3} + 5 x^{9} y^{3} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ Here are the corresponding generator grids to these 24 possibilities:
1 1 2 2 2 2 3 3 3 3 3 3 3 3 3 1 2 2 2 2 2 2 2 2 1 1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 3 3 3 1 1 3 3 3 2 2 3 3 3 1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 3 3 3 1 2 2 2 2 1 3 3 3 1 1 3 3 3 1 1 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 3 3 3 1 1 3 3 3 1 4 4 4 4 1 3 3 3 1 1 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 3 3 3 1 2 2 2 2 4 4 4 4 1 1 4 4 4 4 1 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 3 3 3 1 1 3 3 3 5 5 5 5 5 1 4 4 4 4 1 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 3 3 3 1 2 2 2 2 2 2 2 2 1 3 3 3 1 2 2 3 3 3 1 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 3 3 3 1 1 3 3 3 2 2 3 3 3 3 3 3 1 2 2 3 3 3 1 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 3 3 3 1 2 2 2 2 1 3 3 3 1 4 4 4 4 1 1 3 3 3 1 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 3 3 3 1 1 3 3 3 1 4 4 4 4 4 4 4 4 1 1 3 3 3 1 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 3 3 3 1 2 2 2 2 4 4 4 4 1 5 5 5 5 5 1 3 3 3 1 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 3 3 3 1 1 3 3 3 5 5 5 5 5 5 5 5 5 5 1 3 3 3 1 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 3 3 3 1 2 2 2 2 2 2 2 2 1 1 2 2 2 2 3 3 3 2 2 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 3 3 3 1 1 3 3 3 2 2 3 3 3 1 2 2 2 2 3 3 3 2 2 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 3 3 3 1 2 2 2 2 1 3 3 3 1 1 3 3 3 1 3 3 3 2 2 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 3 3 3 1 1 3 3 3 1 4 4 4 4 1 3 3 3 1 3 3 3 2 2 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 3 3 3 1 2 2 2 2 4 4 4 4 1 1 4 4 4 4 3 3 3 2 2 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 3 3 3 1 1 3 3 3 5 5 5 5 5 1 4 4 4 4 3 3 3 2 2 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 3 3 3 1 2 2 2 2 2 2 2 2 1 3 3 3 2 2 4 4 4 4 1 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 3 3 3 1 1 3 3 3 2 2 3 3 3 3 3 3 2 2 4 4 4 4 1 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 3 3 3 1 2 2 2 2 1 3 3 3 1 4 4 4 4 1 4 4 4 4 1 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 3 3 3 1 1 3 3 3 1 4 4 4 4 4 4 4 4 1 4 4 4 4 1 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 3 3 3 1 2 2 2 2 4 4 4 4 1 5 5 5 5 5 4 4 4 4 1 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 3 3 3 1 1 3 3 3 5 5 5 5 5 5 5 5 5 5 4 4 4 4 1 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1





The AutoKron can't determine the cohomology of $\text{Gr}_2(\mathbb{R}^{11,3})$.

There are 48 possibilities.
Here are their Poincaré polynomials: $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + x^{13} y^{6} + 2 x^{13} y^{5} + x^{12} y^{6} + 2 x^{12} y^{5} + x^{12} y^{4} + 2 x^{11} y^{5} + 2 x^{11} y^{4} + 2 x^{10} y^{5} + 2 x^{10} y^{4} + x^{9} y^{5} + x^{10} y^{3} + 2 x^{9} y^{4} + 2 x^{9} y^{3} + 3 x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + 3 x^{13} y^{5} + x^{12} y^{6} + 3 x^{12} y^{5} + 2 x^{11} y^{5} + 2 x^{11} y^{4} + 2 x^{10} y^{5} + 2 x^{10} y^{4} + x^{9} y^{5} + x^{10} y^{3} + 2 x^{9} y^{4} + 2 x^{9} y^{3} + 3 x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + x^{13} y^{6} + 2 x^{13} y^{5} + 3 x^{12} y^{5} + x^{12} y^{4} + 3 x^{11} y^{5} + x^{11} y^{4} + 2 x^{10} y^{5} + 2 x^{10} y^{4} + x^{9} y^{5} + x^{10} y^{3} + 2 x^{9} y^{4} + 2 x^{9} y^{3} + 3 x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + 3 x^{13} y^{5} + 4 x^{12} y^{5} + 3 x^{11} y^{5} + x^{11} y^{4} + 2 x^{10} y^{5} + 2 x^{10} y^{4} + x^{9} y^{5} + x^{10} y^{3} + 2 x^{9} y^{4} + 2 x^{9} y^{3} + 3 x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + x^{13} y^{6} + 2 x^{13} y^{5} + x^{12} y^{6} + 2 x^{12} y^{5} + x^{12} y^{4} + x^{11} y^{5} + 3 x^{11} y^{4} + 2 x^{10} y^{5} + 3 x^{10} y^{4} + x^{9} y^{5} + 2 x^{9} y^{4} + 2 x^{9} y^{3} + 3 x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + 3 x^{13} y^{5} + x^{12} y^{6} + 3 x^{12} y^{5} + x^{11} y^{5} + 3 x^{11} y^{4} + 2 x^{10} y^{5} + 3 x^{10} y^{4} + x^{9} y^{5} + 2 x^{9} y^{4} + 2 x^{9} y^{3} + 3 x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + x^{13} y^{6} + 2 x^{13} y^{5} + 3 x^{12} y^{5} + x^{12} y^{4} + 2 x^{11} y^{5} + 2 x^{11} y^{4} + 2 x^{10} y^{5} + 3 x^{10} y^{4} + x^{9} y^{5} + 2 x^{9} y^{4} + 2 x^{9} y^{3} + 3 x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + 3 x^{13} y^{5} + 4 x^{12} y^{5} + 2 x^{11} y^{5} + 2 x^{11} y^{4} + 2 x^{10} y^{5} + 3 x^{10} y^{4} + x^{9} y^{5} + 2 x^{9} y^{4} + 2 x^{9} y^{3} + 3 x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + x^{13} y^{6} + 2 x^{13} y^{5} + x^{12} y^{6} + 2 x^{12} y^{5} + x^{12} y^{4} + 2 x^{11} y^{5} + 2 x^{11} y^{4} + x^{10} y^{5} + 3 x^{10} y^{4} + x^{9} y^{5} + x^{10} y^{3} + 3 x^{9} y^{4} + x^{9} y^{3} + 3 x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + 3 x^{13} y^{5} + x^{12} y^{6} + 3 x^{12} y^{5} + 2 x^{11} y^{5} + 2 x^{11} y^{4} + x^{10} y^{5} + 3 x^{10} y^{4} + x^{9} y^{5} + x^{10} y^{3} + 3 x^{9} y^{4} + x^{9} y^{3} + 3 x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + x^{13} y^{6} + 2 x^{13} y^{5} + 3 x^{12} y^{5} + x^{12} y^{4} + 3 x^{11} y^{5} + x^{11} y^{4} + x^{10} y^{5} + 3 x^{10} y^{4} + x^{9} y^{5} + x^{10} y^{3} + 3 x^{9} y^{4} + x^{9} y^{3} + 3 x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + 3 x^{13} y^{5} + 4 x^{12} y^{5} + 3 x^{11} y^{5} + x^{11} y^{4} + x^{10} y^{5} + 3 x^{10} y^{4} + x^{9} y^{5} + x^{10} y^{3} + 3 x^{9} y^{4} + x^{9} y^{3} + 3 x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + x^{13} y^{6} + 2 x^{13} y^{5} + x^{12} y^{6} + 2 x^{12} y^{5} + x^{12} y^{4} + x^{11} y^{5} + 3 x^{11} y^{4} + x^{10} y^{5} + 4 x^{10} y^{4} + x^{9} y^{5} + 3 x^{9} y^{4} + x^{9} y^{3} + 3 x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + 3 x^{13} y^{5} + x^{12} y^{6} + 3 x^{12} y^{5} + x^{11} y^{5} + 3 x^{11} y^{4} + x^{10} y^{5} + 4 x^{10} y^{4} + x^{9} y^{5} + 3 x^{9} y^{4} + x^{9} y^{3} + 3 x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + x^{13} y^{6} + 2 x^{13} y^{5} + 3 x^{12} y^{5} + x^{12} y^{4} + 2 x^{11} y^{5} + 2 x^{11} y^{4} + x^{10} y^{5} + 4 x^{10} y^{4} + x^{9} y^{5} + 3 x^{9} y^{4} + x^{9} y^{3} + 3 x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + 3 x^{13} y^{5} + 4 x^{12} y^{5} + 2 x^{11} y^{5} + 2 x^{11} y^{4} + x^{10} y^{5} + 4 x^{10} y^{4} + x^{9} y^{5} + 3 x^{9} y^{4} + x^{9} y^{3} + 3 x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + x^{13} y^{6} + 2 x^{13} y^{5} + x^{12} y^{6} + 2 x^{12} y^{5} + x^{12} y^{4} + 2 x^{11} y^{5} + 2 x^{11} y^{4} + 4 x^{10} y^{4} + x^{9} y^{5} + x^{10} y^{3} + 4 x^{9} y^{4} + 3 x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + 3 x^{13} y^{5} + x^{12} y^{6} + 3 x^{12} y^{5} + 2 x^{11} y^{5} + 2 x^{11} y^{4} + 4 x^{10} y^{4} + x^{9} y^{5} + x^{10} y^{3} + 4 x^{9} y^{4} + 3 x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + x^{13} y^{6} + 2 x^{13} y^{5} + 3 x^{12} y^{5} + x^{12} y^{4} + 3 x^{11} y^{5} + x^{11} y^{4} + 4 x^{10} y^{4} + x^{9} y^{5} + x^{10} y^{3} + 4 x^{9} y^{4} + 3 x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + 3 x^{13} y^{5} + 4 x^{12} y^{5} + 3 x^{11} y^{5} + x^{11} y^{4} + 4 x^{10} y^{4} + x^{9} y^{5} + x^{10} y^{3} + 4 x^{9} y^{4} + 3 x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + x^{13} y^{6} + 2 x^{13} y^{5} + x^{12} y^{6} + 2 x^{12} y^{5} + x^{12} y^{4} + x^{11} y^{5} + 3 x^{11} y^{4} + 5 x^{10} y^{4} + x^{9} y^{5} + 4 x^{9} y^{4} + 3 x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + 3 x^{13} y^{5} + x^{12} y^{6} + 3 x^{12} y^{5} + x^{11} y^{5} + 3 x^{11} y^{4} + 5 x^{10} y^{4} + x^{9} y^{5} + 4 x^{9} y^{4} + 3 x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + x^{13} y^{6} + 2 x^{13} y^{5} + 3 x^{12} y^{5} + x^{12} y^{4} + 2 x^{11} y^{5} + 2 x^{11} y^{4} + 5 x^{10} y^{4} + x^{9} y^{5} + 4 x^{9} y^{4} + 3 x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + 3 x^{13} y^{5} + 4 x^{12} y^{5} + 2 x^{11} y^{5} + 2 x^{11} y^{4} + 5 x^{10} y^{4} + x^{9} y^{5} + 4 x^{9} y^{4} + 3 x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + x^{13} y^{6} + 2 x^{13} y^{5} + x^{12} y^{6} + 2 x^{12} y^{5} + x^{12} y^{4} + 2 x^{11} y^{5} + 2 x^{11} y^{4} + 2 x^{10} y^{5} + 2 x^{10} y^{4} + x^{10} y^{3} + 3 x^{9} y^{4} + 2 x^{9} y^{3} + 4 x^{8} y^{4} + x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + 3 x^{13} y^{5} + x^{12} y^{6} + 3 x^{12} y^{5} + 2 x^{11} y^{5} + 2 x^{11} y^{4} + 2 x^{10} y^{5} + 2 x^{10} y^{4} + x^{10} y^{3} + 3 x^{9} y^{4} + 2 x^{9} y^{3} + 4 x^{8} y^{4} + x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + x^{13} y^{6} + 2 x^{13} y^{5} + 3 x^{12} y^{5} + x^{12} y^{4} + 3 x^{11} y^{5} + x^{11} y^{4} + 2 x^{10} y^{5} + 2 x^{10} y^{4} + x^{10} y^{3} + 3 x^{9} y^{4} + 2 x^{9} y^{3} + 4 x^{8} y^{4} + x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + 3 x^{13} y^{5} + 4 x^{12} y^{5} + 3 x^{11} y^{5} + x^{11} y^{4} + 2 x^{10} y^{5} + 2 x^{10} y^{4} + x^{10} y^{3} + 3 x^{9} y^{4} + 2 x^{9} y^{3} + 4 x^{8} y^{4} + x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + x^{13} y^{6} + 2 x^{13} y^{5} + x^{12} y^{6} + 2 x^{12} y^{5} + x^{12} y^{4} + x^{11} y^{5} + 3 x^{11} y^{4} + 2 x^{10} y^{5} + 3 x^{10} y^{4} + 3 x^{9} y^{4} + 2 x^{9} y^{3} + 4 x^{8} y^{4} + x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + 3 x^{13} y^{5} + x^{12} y^{6} + 3 x^{12} y^{5} + x^{11} y^{5} + 3 x^{11} y^{4} + 2 x^{10} y^{5} + 3 x^{10} y^{4} + 3 x^{9} y^{4} + 2 x^{9} y^{3} + 4 x^{8} y^{4} + x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + x^{13} y^{6} + 2 x^{13} y^{5} + 3 x^{12} y^{5} + x^{12} y^{4} + 2 x^{11} y^{5} + 2 x^{11} y^{4} + 2 x^{10} y^{5} + 3 x^{10} y^{4} + 3 x^{9} y^{4} + 2 x^{9} y^{3} + 4 x^{8} y^{4} + x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + 3 x^{13} y^{5} + 4 x^{12} y^{5} + 2 x^{11} y^{5} + 2 x^{11} y^{4} + 2 x^{10} y^{5} + 3 x^{10} y^{4} + 3 x^{9} y^{4} + 2 x^{9} y^{3} + 4 x^{8} y^{4} + x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + x^{13} y^{6} + 2 x^{13} y^{5} + x^{12} y^{6} + 2 x^{12} y^{5} + x^{12} y^{4} + 2 x^{11} y^{5} + 2 x^{11} y^{4} + x^{10} y^{5} + 3 x^{10} y^{4} + x^{10} y^{3} + 4 x^{9} y^{4} + x^{9} y^{3} + 4 x^{8} y^{4} + x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + 3 x^{13} y^{5} + x^{12} y^{6} + 3 x^{12} y^{5} + 2 x^{11} y^{5} + 2 x^{11} y^{4} + x^{10} y^{5} + 3 x^{10} y^{4} + x^{10} y^{3} + 4 x^{9} y^{4} + x^{9} y^{3} + 4 x^{8} y^{4} + x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + x^{13} y^{6} + 2 x^{13} y^{5} + 3 x^{12} y^{5} + x^{12} y^{4} + 3 x^{11} y^{5} + x^{11} y^{4} + x^{10} y^{5} + 3 x^{10} y^{4} + x^{10} y^{3} + 4 x^{9} y^{4} + x^{9} y^{3} + 4 x^{8} y^{4} + x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + 3 x^{13} y^{5} + 4 x^{12} y^{5} + 3 x^{11} y^{5} + x^{11} y^{4} + x^{10} y^{5} + 3 x^{10} y^{4} + x^{10} y^{3} + 4 x^{9} y^{4} + x^{9} y^{3} + 4 x^{8} y^{4} + x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + x^{13} y^{6} + 2 x^{13} y^{5} + x^{12} y^{6} + 2 x^{12} y^{5} + x^{12} y^{4} + x^{11} y^{5} + 3 x^{11} y^{4} + x^{10} y^{5} + 4 x^{10} y^{4} + 4 x^{9} y^{4} + x^{9} y^{3} + 4 x^{8} y^{4} + x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + 3 x^{13} y^{5} + x^{12} y^{6} + 3 x^{12} y^{5} + x^{11} y^{5} + 3 x^{11} y^{4} + x^{10} y^{5} + 4 x^{10} y^{4} + 4 x^{9} y^{4} + x^{9} y^{3} + 4 x^{8} y^{4} + x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + x^{13} y^{6} + 2 x^{13} y^{5} + 3 x^{12} y^{5} + x^{12} y^{4} + 2 x^{11} y^{5} + 2 x^{11} y^{4} + x^{10} y^{5} + 4 x^{10} y^{4} + 4 x^{9} y^{4} + x^{9} y^{3} + 4 x^{8} y^{4} + x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + 3 x^{13} y^{5} + 4 x^{12} y^{5} + 2 x^{11} y^{5} + 2 x^{11} y^{4} + x^{10} y^{5} + 4 x^{10} y^{4} + 4 x^{9} y^{4} + x^{9} y^{3} + 4 x^{8} y^{4} + x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + x^{13} y^{6} + 2 x^{13} y^{5} + x^{12} y^{6} + 2 x^{12} y^{5} + x^{12} y^{4} + 2 x^{11} y^{5} + 2 x^{11} y^{4} + 4 x^{10} y^{4} + x^{10} y^{3} + 5 x^{9} y^{4} + 4 x^{8} y^{4} + x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + 3 x^{13} y^{5} + x^{12} y^{6} + 3 x^{12} y^{5} + 2 x^{11} y^{5} + 2 x^{11} y^{4} + 4 x^{10} y^{4} + x^{10} y^{3} + 5 x^{9} y^{4} + 4 x^{8} y^{4} + x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + x^{13} y^{6} + 2 x^{13} y^{5} + 3 x^{12} y^{5} + x^{12} y^{4} + 3 x^{11} y^{5} + x^{11} y^{4} + 4 x^{10} y^{4} + x^{10} y^{3} + 5 x^{9} y^{4} + 4 x^{8} y^{4} + x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + 3 x^{13} y^{5} + 4 x^{12} y^{5} + 3 x^{11} y^{5} + x^{11} y^{4} + 4 x^{10} y^{4} + x^{10} y^{3} + 5 x^{9} y^{4} + 4 x^{8} y^{4} + x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + x^{13} y^{6} + 2 x^{13} y^{5} + x^{12} y^{6} + 2 x^{12} y^{5} + x^{12} y^{4} + x^{11} y^{5} + 3 x^{11} y^{4} + 5 x^{10} y^{4} + 5 x^{9} y^{4} + 4 x^{8} y^{4} + x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + 3 x^{13} y^{5} + x^{12} y^{6} + 3 x^{12} y^{5} + x^{11} y^{5} + 3 x^{11} y^{4} + 5 x^{10} y^{4} + 5 x^{9} y^{4} + 4 x^{8} y^{4} + x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + x^{13} y^{6} + 2 x^{13} y^{5} + 3 x^{12} y^{5} + x^{12} y^{4} + 2 x^{11} y^{5} + 2 x^{11} y^{4} + 5 x^{10} y^{4} + 5 x^{9} y^{4} + 4 x^{8} y^{4} + x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{6} + x^{17} y^{6} + 2 x^{16} y^{6} + 2 x^{15} y^{6} + 2 x^{14} y^{6} + x^{14} y^{5} + 3 x^{13} y^{5} + 4 x^{12} y^{5} + 2 x^{11} y^{5} + 2 x^{11} y^{4} + 5 x^{10} y^{4} + 5 x^{9} y^{4} + 4 x^{8} y^{4} + x^{8} y^{3} + 2 x^{7} y^{4} + 2 x^{7} y^{3} + x^{6} y^{4} + 3 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ Here are the corresponding generator grids to these 48 possibilities:
1 1 2 2 2 2 2 2 1 1 2 2 1 2 2 1 2 2 2 2 2 2 2 2 1 1 2 2 2 2 3 3 3 2 2 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 3 3 3 1 3 3 3 2 2 2 2 2 2 2 2 1 1 2 2 2 2 3 3 3 2 2 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 1 2 2 3 3 3 1 3 3 3 1 2 2 2 2 1 1 2 2 2 2 3 3 3 2 2 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 3 3 3 4 4 4 4 3 3 3 1 2 2 2 2 1 1 2 2 2 2 3 3 3 2 2 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 1 2 2 1 2 2 1 1 3 3 3 2 2 3 3 3 1 2 2 2 2 3 3 3 2 2 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 3 3 3 1 3 3 3 1 3 3 3 2 2 3 3 3 1 2 2 2 2 3 3 3 2 2 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 1 2 2 3 3 3 1 2 2 2 2 2 2 3 3 3 1 2 2 2 2 3 3 3 2 2 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 3 3 3 4 4 4 4 2 2 2 2 2 2 3 3 3 1 2 2 2 2 3 3 3 2 2 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 1 2 2 1 2 2 1 2 2 2 2 1 3 3 3 1 1 3 3 3 1 3 3 3 2 2 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 3 3 3 1 3 3 3 2 2 2 2 1 3 3 3 1 1 3 3 3 1 3 3 3 2 2 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 1 2 2 3 3 3 1 3 3 3 1 1 3 3 3 1 1 3 3 3 1 3 3 3 2 2 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 3 3 3 4 4 4 4 3 3 3 1 1 3 3 3 1 1 3 3 3 1 3 3 3 2 2 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 1 2 2 1 2 2 1 1 3 3 3 1 4 4 4 4 1 3 3 3 1 3 3 3 2 2 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 3 3 3 1 3 3 3 1 3 3 3 1 4 4 4 4 1 3 3 3 1 3 3 3 2 2 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 1 2 2 3 3 3 1 2 2 2 2 1 4 4 4 4 1 3 3 3 1 3 3 3 2 2 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 3 3 3 4 4 4 4 2 2 2 2 1 4 4 4 4 1 3 3 3 1 3 3 3 2 2 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 1 2 2 1 2 2 1 2 2 2 2 4 4 4 4 1 1 4 4 4 4 3 3 3 2 2 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 3 3 3 1 3 3 3 2 2 2 2 4 4 4 4 1 1 4 4 4 4 3 3 3 2 2 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 1 2 2 3 3 3 1 3 3 3 1 4 4 4 4 1 1 4 4 4 4 3 3 3 2 2 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 3 3 3 4 4 4 4 3 3 3 1 4 4 4 4 1 1 4 4 4 4 3 3 3 2 2 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 1 2 2 1 2 2 1 1 3 3 3 5 5 5 5 5 1 4 4 4 4 3 3 3 2 2 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 3 3 3 1 3 3 3 1 3 3 3 5 5 5 5 5 1 4 4 4 4 3 3 3 2 2 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 1 2 2 3 3 3 1 2 2 2 2 5 5 5 5 5 1 4 4 4 4 3 3 3 2 2 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 3 3 3 4 4 4 4 2 2 2 2 5 5 5 5 5 1 4 4 4 4 3 3 3 2 2 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 1 2 2 1 2 2 1 2 2 2 2 2 2 2 2 1 3 3 3 2 2 4 4 4 4 1 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 3 3 3 1 3 3 3 2 2 2 2 2 2 2 2 1 3 3 3 2 2 4 4 4 4 1 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 1 2 2 3 3 3 1 3 3 3 1 2 2 2 2 1 3 3 3 2 2 4 4 4 4 1 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 3 3 3 4 4 4 4 3 3 3 1 2 2 2 2 1 3 3 3 2 2 4 4 4 4 1 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 1 2 2 1 2 2 1 1 3 3 3 2 2 3 3 3 3 3 3 2 2 4 4 4 4 1 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 3 3 3 1 3 3 3 1 3 3 3 2 2 3 3 3 3 3 3 2 2 4 4 4 4 1 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 1 2 2 3 3 3 1 2 2 2 2 2 2 3 3 3 3 3 3 2 2 4 4 4 4 1 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 3 3 3 4 4 4 4 2 2 2 2 2 2 3 3 3 3 3 3 2 2 4 4 4 4 1 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 1 2 2 1 2 2 1 2 2 2 2 1 3 3 3 1 4 4 4 4 1 4 4 4 4 1 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 3 3 3 1 3 3 3 2 2 2 2 1 3 3 3 1 4 4 4 4 1 4 4 4 4 1 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 1 2 2 3 3 3 1 3 3 3 1 1 3 3 3 1 4 4 4 4 1 4 4 4 4 1 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 3 3 3 4 4 4 4 3 3 3 1 1 3 3 3 1 4 4 4 4 1 4 4 4 4 1 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 1 2 2 1 2 2 1 1 3 3 3 1 4 4 4 4 4 4 4 4 1 4 4 4 4 1 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 3 3 3 1 3 3 3 1 3 3 3 1 4 4 4 4 4 4 4 4 1 4 4 4 4 1 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 1 2 2 3 3 3 1 2 2 2 2 1 4 4 4 4 4 4 4 4 1 4 4 4 4 1 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 3 3 3 4 4 4 4 2 2 2 2 1 4 4 4 4 4 4 4 4 1 4 4 4 4 1 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 1 2 2 1 2 2 1 2 2 2 2 4 4 4 4 1 5 5 5 5 5 4 4 4 4 1 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 3 3 3 1 3 3 3 2 2 2 2 4 4 4 4 1 5 5 5 5 5 4 4 4 4 1 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 1 2 2 3 3 3 1 3 3 3 1 4 4 4 4 1 5 5 5 5 5 4 4 4 4 1 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 3 3 3 4 4 4 4 3 3 3 1 4 4 4 4 1 5 5 5 5 5 4 4 4 4 1 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 1 2 2 1 2 2 1 1 3 3 3 5 5 5 5 5 5 5 5 5 5 4 4 4 4 1 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 3 3 3 1 3 3 3 1 3 3 3 5 5 5 5 5 5 5 5 5 5 4 4 4 4 1 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 1 2 2 3 3 3 1 2 2 2 2 5 5 5 5 5 5 5 5 5 5 4 4 4 4 1 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 2 2 2 2 1 3 3 3 4 4 4 4 2 2 2 2 5 5 5 5 5 5 5 5 5 5 4 4 4 4 1 2 2 2 2 1 3 3 3 3 3 3 1 2 2 2 2 1 1 1 1





The AutoKron can't determine the cohomology of $\text{Gr}_2(\mathbb{R}^{11,4})$.

There are 8 possibilities.
Here are their Poincaré polynomials: $$x^{18} y^{8} + x^{17} y^{8} + x^{16} y^{8} + x^{16} y^{7} + 2 x^{15} y^{7} + 2 x^{14} y^{7} + x^{14} y^{6} + x^{13} y^{7} + 2 x^{13} y^{6} + 3 x^{12} y^{6} + x^{12} y^{5} + 2 x^{11} y^{6} + 2 x^{11} y^{5} + x^{10} y^{6} + 3 x^{10} y^{5} + x^{10} y^{4} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{8} + x^{17} y^{8} + x^{16} y^{8} + x^{16} y^{7} + 2 x^{15} y^{7} + 2 x^{14} y^{7} + x^{14} y^{6} + 3 x^{13} y^{6} + 4 x^{12} y^{6} + 2 x^{11} y^{6} + 2 x^{11} y^{5} + x^{10} y^{6} + 3 x^{10} y^{5} + x^{10} y^{4} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{8} + x^{17} y^{8} + x^{16} y^{8} + x^{16} y^{7} + 2 x^{15} y^{7} + 2 x^{14} y^{7} + x^{14} y^{6} + x^{13} y^{7} + 2 x^{13} y^{6} + 3 x^{12} y^{6} + x^{12} y^{5} + x^{11} y^{6} + 3 x^{11} y^{5} + x^{10} y^{6} + 4 x^{10} y^{5} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{8} + x^{17} y^{8} + x^{16} y^{8} + x^{16} y^{7} + 2 x^{15} y^{7} + 2 x^{14} y^{7} + x^{14} y^{6} + 3 x^{13} y^{6} + 4 x^{12} y^{6} + x^{11} y^{6} + 3 x^{11} y^{5} + x^{10} y^{6} + 4 x^{10} y^{5} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{8} + x^{17} y^{8} + x^{16} y^{8} + x^{16} y^{7} + 2 x^{15} y^{7} + 2 x^{14} y^{7} + x^{14} y^{6} + x^{13} y^{7} + 2 x^{13} y^{6} + 3 x^{12} y^{6} + x^{12} y^{5} + 2 x^{11} y^{6} + 2 x^{11} y^{5} + 4 x^{10} y^{5} + x^{10} y^{4} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{8} + x^{17} y^{8} + x^{16} y^{8} + x^{16} y^{7} + 2 x^{15} y^{7} + 2 x^{14} y^{7} + x^{14} y^{6} + 3 x^{13} y^{6} + 4 x^{12} y^{6} + 2 x^{11} y^{6} + 2 x^{11} y^{5} + 4 x^{10} y^{5} + x^{10} y^{4} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{8} + x^{17} y^{8} + x^{16} y^{8} + x^{16} y^{7} + 2 x^{15} y^{7} + 2 x^{14} y^{7} + x^{14} y^{6} + x^{13} y^{7} + 2 x^{13} y^{6} + 3 x^{12} y^{6} + x^{12} y^{5} + x^{11} y^{6} + 3 x^{11} y^{5} + 5 x^{10} y^{5} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{18} y^{8} + x^{17} y^{8} + x^{16} y^{8} + x^{16} y^{7} + 2 x^{15} y^{7} + 2 x^{14} y^{7} + x^{14} y^{6} + 3 x^{13} y^{6} + 4 x^{12} y^{6} + x^{11} y^{6} + 3 x^{11} y^{5} + 5 x^{10} y^{5} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ Here are the corresponding generator grids to these 8 possibilities:
1 1 1 1 2 2 2 2 1 1 2 2 3 3 3 1 2 2 2 2 1 3 3 3 1 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 1 1 2 2 2 2 1 3 3 3 4 4 4 4 2 2 2 2 1 3 3 3 1 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 1 1 2 2 2 2 1 1 2 2 3 3 3 1 1 3 3 3 1 4 4 4 4 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 1 1 2 2 2 2 1 3 3 3 4 4 4 4 1 3 3 3 1 4 4 4 4 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 1 1 2 2 2 2 1 1 2 2 3 3 3 1 2 2 2 2 4 4 4 4 1 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 1 1 2 2 2 2 1 3 3 3 4 4 4 4 2 2 2 2 4 4 4 4 1 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 1 1 2 2 2 2 1 1 2 2 3 3 3 1 1 3 3 3 5 5 5 5 5 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 1 1 2 2 2 2 1 3 3 3 4 4 4 4 1 3 3 3 5 5 5 5 5 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1





The cohomology of $\text{Gr}_2(\mathbb{R}^{11,5})$

Poincaré polynomial: $$x^{18} y^{9} + x^{17} y^{9} + 2 x^{16} y^{8} + 2 x^{15} y^{8} + x^{14} y^{8} + 2 x^{14} y^{7} + 3 x^{13} y^{7} + x^{12} y^{7} + 3 x^{12} y^{6} + 4 x^{11} y^{6} + 2 x^{10} y^{6} + 3 x^{10} y^{5} + 5 x^{9} y^{5} + 2 x^{8} y^{5} + 3 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ Generator count grid:
1 1 2 2 2 2 1 2 2 3 3 3 1 3 3 3 4 4 4 4 2 2 3 3 3 5 5 5 5 5 2 2 3 3 3 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
Explicitly, as a free module over the ground ring $\mathbb{M}_2$: $$H^{\ast,\ast}(\text{Gr}_2(\mathbb{R}^{11,5}))=\mathbb{M}_2\oplus\Sigma^{1,1}\mathbb{M}_2\oplus\Sigma^{2,1}\mathbb{M}_2\oplus\Sigma^{2,2}\mathbb{M}_2\oplus\Sigma^{3,2}\mathbb{M}_2\oplus\Sigma^{4,2}\mathbb{M}_2\oplus\Sigma^{4,3}\mathbb{M}_2\oplus\Sigma^{5,3}\mathbb{M}_2\oplus\Sigma^{6,3}\mathbb{M}_2\oplus\Sigma^{6,4}\mathbb{M}_2\oplus\Sigma^{7,4}\mathbb{M}_2\oplus\Sigma^{8,4}\mathbb{M}_2\oplus\Sigma^{8,5}\mathbb{M}_2\oplus\Sigma^{9,5}\mathbb{M}_2\oplus\Sigma^{10,5}\mathbb{M}_2\oplus\Sigma^{10,6}\mathbb{M}_2\oplus\Sigma^{11,6}\mathbb{M}_2\oplus\Sigma^{12,6}\mathbb{M}_2\oplus\Sigma^{12,7}\mathbb{M}_2\oplus\Sigma^{13,7}\mathbb{M}_2\oplus\Sigma^{14,7}\mathbb{M}_2\oplus\Sigma^{14,8}\mathbb{M}_2\oplus\Sigma^{15,8}\mathbb{M}_2\oplus\Sigma^{16,8}\mathbb{M}_2\oplus\Sigma^{17,9}\mathbb{M}_2\oplus\Sigma^{18,9}\mathbb{M}_2.$$




The cohomology of $\text{Gr}_2(\mathbb{R}^{12,1})$

Poincaré polynomial: $$x^{20} y^{2} + x^{19} y^{2} + 2 x^{18} y^{2} + 2 x^{17} y^{2} + 3 x^{16} y^{2} + 3 x^{15} y^{2} + 4 x^{14} y^{2} + 4 x^{13} y^{2} + 5 x^{12} y^{2} + 4 x^{11} y^{2} + x^{11} y + 4 x^{10} y^{2} + 2 x^{10} y + 3 x^{9} y^{2} + 2 x^{9} y + 3 x^{8} y^{2} + 2 x^{8} y + 2 x^{7} y^{2} + 2 x^{7} y + 2 x^{6} y^{2} + 2 x^{6} y + x^{5} y^{2} + 2 x^{5} y + x^{4} y^{2} + 2 x^{4} y + 2 x^{3} y + 2 x^{2} y + x y + 1$$ Generator count grid:
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 4 4 5 5 5 5 5 4 4 4 4 1 4 4 4 4 2 2 3 3 3 2 2 3 3 3 2 2 2 2 2 2 2 2 2 2 1 2 2 1 2 2 2 2 2 2 1 1
Explicitly, as a free module over the ground ring $\mathbb{M}_2$: $$H^{\ast,\ast}(\text{Gr}_2(\mathbb{R}^{12,1}))=\mathbb{M}_2\oplus\Sigma^{1,1}\mathbb{M}_2\oplus\Sigma^{2,1}\mathbb{M}_2\oplus\Sigma^{3,1}\mathbb{M}_2\oplus\Sigma^{4,1}\mathbb{M}_2\oplus\Sigma^{4,2}\mathbb{M}_2\oplus\Sigma^{5,1}\mathbb{M}_2\oplus\Sigma^{5,2}\mathbb{M}_2\oplus\Sigma^{6,1}\mathbb{M}_2\oplus\Sigma^{6,2}\mathbb{M}_2\oplus\Sigma^{7,1}\mathbb{M}_2\oplus\Sigma^{7,2}\mathbb{M}_2\oplus\Sigma^{8,1}\mathbb{M}_2\oplus\Sigma^{8,2}\mathbb{M}_2\oplus\Sigma^{9,1}\mathbb{M}_2\oplus\Sigma^{9,2}\mathbb{M}_2\oplus\Sigma^{10,1}\mathbb{M}_2\oplus\Sigma^{10,2}\mathbb{M}_2\oplus\Sigma^{11,1}\mathbb{M}_2\oplus\Sigma^{11,2}\mathbb{M}_2\oplus\Sigma^{12,2}\mathbb{M}_2\oplus\Sigma^{13,2}\mathbb{M}_2\oplus\Sigma^{14,2}\mathbb{M}_2\oplus\Sigma^{15,2}\mathbb{M}_2\oplus\Sigma^{16,2}\mathbb{M}_2\oplus\Sigma^{17,2}\mathbb{M}_2\oplus\Sigma^{18,2}\mathbb{M}_2\oplus\Sigma^{19,2}\mathbb{M}_2\oplus\Sigma^{20,2}\mathbb{M}_2.$$




The AutoKron can't determine the cohomology of $\text{Gr}_2(\mathbb{R}^{12,2})$.

There are 72 possibilities.
Here are their Poincaré polynomials: $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + 2 x^{10} y^{4} + x^{11} y^{2} + 2 x^{10} y^{3} + x^{9} y^{4} + 2 x^{10} y^{2} + 2 x^{9} y^{3} + x^{8} y^{4} + 2 x^{9} y^{2} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 2 x^{11} y^{4} + 3 x^{11} y^{3} + 2 x^{10} y^{4} + 2 x^{10} y^{3} + x^{9} y^{4} + 2 x^{10} y^{2} + 2 x^{9} y^{3} + x^{8} y^{4} + 2 x^{9} y^{2} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + 2 x^{10} y^{4} + x^{11} y^{2} + 3 x^{10} y^{3} + x^{9} y^{4} + x^{10} y^{2} + 2 x^{9} y^{3} + x^{8} y^{4} + 2 x^{9} y^{2} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + x^{11} y^{4} + 4 x^{11} y^{3} + 2 x^{10} y^{4} + 3 x^{10} y^{3} + x^{9} y^{4} + x^{10} y^{2} + 2 x^{9} y^{3} + x^{8} y^{4} + 2 x^{9} y^{2} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 4 x^{11} y^{3} + 2 x^{10} y^{4} + x^{11} y^{2} + 4 x^{10} y^{3} + x^{9} y^{4} + 2 x^{9} y^{3} + x^{8} y^{4} + 2 x^{9} y^{2} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 5 x^{11} y^{3} + 2 x^{10} y^{4} + 4 x^{10} y^{3} + x^{9} y^{4} + 2 x^{9} y^{3} + x^{8} y^{4} + 2 x^{9} y^{2} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + x^{10} y^{4} + x^{11} y^{2} + 3 x^{10} y^{3} + x^{9} y^{4} + 2 x^{10} y^{2} + 3 x^{9} y^{3} + x^{8} y^{4} + x^{9} y^{2} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 2 x^{11} y^{4} + 3 x^{11} y^{3} + x^{10} y^{4} + 3 x^{10} y^{3} + x^{9} y^{4} + 2 x^{10} y^{2} + 3 x^{9} y^{3} + x^{8} y^{4} + x^{9} y^{2} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + x^{10} y^{4} + x^{11} y^{2} + 4 x^{10} y^{3} + x^{9} y^{4} + x^{10} y^{2} + 3 x^{9} y^{3} + x^{8} y^{4} + x^{9} y^{2} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + x^{11} y^{4} + 4 x^{11} y^{3} + x^{10} y^{4} + 4 x^{10} y^{3} + x^{9} y^{4} + x^{10} y^{2} + 3 x^{9} y^{3} + x^{8} y^{4} + x^{9} y^{2} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 4 x^{11} y^{3} + x^{10} y^{4} + x^{11} y^{2} + 5 x^{10} y^{3} + x^{9} y^{4} + 3 x^{9} y^{3} + x^{8} y^{4} + x^{9} y^{2} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 5 x^{11} y^{3} + x^{10} y^{4} + 5 x^{10} y^{3} + x^{9} y^{4} + 3 x^{9} y^{3} + x^{8} y^{4} + x^{9} y^{2} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + x^{11} y^{2} + 4 x^{10} y^{3} + x^{9} y^{4} + 2 x^{10} y^{2} + 4 x^{9} y^{3} + x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 2 x^{11} y^{4} + 3 x^{11} y^{3} + 4 x^{10} y^{3} + x^{9} y^{4} + 2 x^{10} y^{2} + 4 x^{9} y^{3} + x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + x^{11} y^{2} + 5 x^{10} y^{3} + x^{9} y^{4} + x^{10} y^{2} + 4 x^{9} y^{3} + x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + x^{11} y^{4} + 4 x^{11} y^{3} + 5 x^{10} y^{3} + x^{9} y^{4} + x^{10} y^{2} + 4 x^{9} y^{3} + x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 4 x^{11} y^{3} + x^{11} y^{2} + 6 x^{10} y^{3} + x^{9} y^{4} + 4 x^{9} y^{3} + x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 5 x^{11} y^{3} + 6 x^{10} y^{3} + x^{9} y^{4} + 4 x^{9} y^{3} + x^{8} y^{4} + 2 x^{8} y^{3} + 2 x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + 2 x^{10} y^{4} + x^{11} y^{2} + 2 x^{10} y^{3} + 2 x^{10} y^{2} + 3 x^{9} y^{3} + x^{8} y^{4} + 2 x^{9} y^{2} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 2 x^{11} y^{4} + 3 x^{11} y^{3} + 2 x^{10} y^{4} + 2 x^{10} y^{3} + 2 x^{10} y^{2} + 3 x^{9} y^{3} + x^{8} y^{4} + 2 x^{9} y^{2} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + 2 x^{10} y^{4} + x^{11} y^{2} + 3 x^{10} y^{3} + x^{10} y^{2} + 3 x^{9} y^{3} + x^{8} y^{4} + 2 x^{9} y^{2} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + x^{11} y^{4} + 4 x^{11} y^{3} + 2 x^{10} y^{4} + 3 x^{10} y^{3} + x^{10} y^{2} + 3 x^{9} y^{3} + x^{8} y^{4} + 2 x^{9} y^{2} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 4 x^{11} y^{3} + 2 x^{10} y^{4} + x^{11} y^{2} + 4 x^{10} y^{3} + 3 x^{9} y^{3} + x^{8} y^{4} + 2 x^{9} y^{2} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 5 x^{11} y^{3} + 2 x^{10} y^{4} + 4 x^{10} y^{3} + 3 x^{9} y^{3} + x^{8} y^{4} + 2 x^{9} y^{2} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + x^{10} y^{4} + x^{11} y^{2} + 3 x^{10} y^{3} + 2 x^{10} y^{2} + 4 x^{9} y^{3} + x^{8} y^{4} + x^{9} y^{2} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 2 x^{11} y^{4} + 3 x^{11} y^{3} + x^{10} y^{4} + 3 x^{10} y^{3} + 2 x^{10} y^{2} + 4 x^{9} y^{3} + x^{8} y^{4} + x^{9} y^{2} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + x^{10} y^{4} + x^{11} y^{2} + 4 x^{10} y^{3} + x^{10} y^{2} + 4 x^{9} y^{3} + x^{8} y^{4} + x^{9} y^{2} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + x^{11} y^{4} + 4 x^{11} y^{3} + x^{10} y^{4} + 4 x^{10} y^{3} + x^{10} y^{2} + 4 x^{9} y^{3} + x^{8} y^{4} + x^{9} y^{2} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 4 x^{11} y^{3} + x^{10} y^{4} + x^{11} y^{2} + 5 x^{10} y^{3} + 4 x^{9} y^{3} + x^{8} y^{4} + x^{9} y^{2} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 5 x^{11} y^{3} + x^{10} y^{4} + 5 x^{10} y^{3} + 4 x^{9} y^{3} + x^{8} y^{4} + x^{9} y^{2} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + x^{11} y^{2} + 4 x^{10} y^{3} + 2 x^{10} y^{2} + 5 x^{9} y^{3} + x^{8} y^{4} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 2 x^{11} y^{4} + 3 x^{11} y^{3} + 4 x^{10} y^{3} + 2 x^{10} y^{2} + 5 x^{9} y^{3} + x^{8} y^{4} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + x^{11} y^{2} + 5 x^{10} y^{3} + x^{10} y^{2} + 5 x^{9} y^{3} + x^{8} y^{4} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + x^{11} y^{4} + 4 x^{11} y^{3} + 5 x^{10} y^{3} + x^{10} y^{2} + 5 x^{9} y^{3} + x^{8} y^{4} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 4 x^{11} y^{3} + x^{11} y^{2} + 6 x^{10} y^{3} + 5 x^{9} y^{3} + x^{8} y^{4} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 5 x^{11} y^{3} + 6 x^{10} y^{3} + 5 x^{9} y^{3} + x^{8} y^{4} + 3 x^{8} y^{3} + x^{8} y^{2} + 2 x^{7} y^{3} + 2 x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + 2 x^{10} y^{4} + x^{11} y^{2} + 2 x^{10} y^{3} + x^{9} y^{4} + 2 x^{10} y^{2} + 2 x^{9} y^{3} + 2 x^{9} y^{2} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 2 x^{11} y^{4} + 3 x^{11} y^{3} + 2 x^{10} y^{4} + 2 x^{10} y^{3} + x^{9} y^{4} + 2 x^{10} y^{2} + 2 x^{9} y^{3} + 2 x^{9} y^{2} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + 2 x^{10} y^{4} + x^{11} y^{2} + 3 x^{10} y^{3} + x^{9} y^{4} + x^{10} y^{2} + 2 x^{9} y^{3} + 2 x^{9} y^{2} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + x^{11} y^{4} + 4 x^{11} y^{3} + 2 x^{10} y^{4} + 3 x^{10} y^{3} + x^{9} y^{4} + x^{10} y^{2} + 2 x^{9} y^{3} + 2 x^{9} y^{2} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 4 x^{11} y^{3} + 2 x^{10} y^{4} + x^{11} y^{2} + 4 x^{10} y^{3} + x^{9} y^{4} + 2 x^{9} y^{3} + 2 x^{9} y^{2} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 5 x^{11} y^{3} + 2 x^{10} y^{4} + 4 x^{10} y^{3} + x^{9} y^{4} + 2 x^{9} y^{3} + 2 x^{9} y^{2} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + x^{10} y^{4} + x^{11} y^{2} + 3 x^{10} y^{3} + x^{9} y^{4} + 2 x^{10} y^{2} + 3 x^{9} y^{3} + x^{9} y^{2} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 2 x^{11} y^{4} + 3 x^{11} y^{3} + x^{10} y^{4} + 3 x^{10} y^{3} + x^{9} y^{4} + 2 x^{10} y^{2} + 3 x^{9} y^{3} + x^{9} y^{2} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + x^{10} y^{4} + x^{11} y^{2} + 4 x^{10} y^{3} + x^{9} y^{4} + x^{10} y^{2} + 3 x^{9} y^{3} + x^{9} y^{2} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + x^{11} y^{4} + 4 x^{11} y^{3} + x^{10} y^{4} + 4 x^{10} y^{3} + x^{9} y^{4} + x^{10} y^{2} + 3 x^{9} y^{3} + x^{9} y^{2} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 4 x^{11} y^{3} + x^{10} y^{4} + x^{11} y^{2} + 5 x^{10} y^{3} + x^{9} y^{4} + 3 x^{9} y^{3} + x^{9} y^{2} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 5 x^{11} y^{3} + x^{10} y^{4} + 5 x^{10} y^{3} + x^{9} y^{4} + 3 x^{9} y^{3} + x^{9} y^{2} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + x^{11} y^{2} + 4 x^{10} y^{3} + x^{9} y^{4} + 2 x^{10} y^{2} + 4 x^{9} y^{3} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 2 x^{11} y^{4} + 3 x^{11} y^{3} + 4 x^{10} y^{3} + x^{9} y^{4} + 2 x^{10} y^{2} + 4 x^{9} y^{3} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + x^{11} y^{2} + 5 x^{10} y^{3} + x^{9} y^{4} + x^{10} y^{2} + 4 x^{9} y^{3} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + x^{11} y^{4} + 4 x^{11} y^{3} + 5 x^{10} y^{3} + x^{9} y^{4} + x^{10} y^{2} + 4 x^{9} y^{3} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 4 x^{11} y^{3} + x^{11} y^{2} + 6 x^{10} y^{3} + x^{9} y^{4} + 4 x^{9} y^{3} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 5 x^{11} y^{3} + 6 x^{10} y^{3} + x^{9} y^{4} + 4 x^{9} y^{3} + 3 x^{8} y^{3} + 2 x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + 2 x^{10} y^{4} + x^{11} y^{2} + 2 x^{10} y^{3} + 2 x^{10} y^{2} + 3 x^{9} y^{3} + 2 x^{9} y^{2} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 2 x^{11} y^{4} + 3 x^{11} y^{3} + 2 x^{10} y^{4} + 2 x^{10} y^{3} + 2 x^{10} y^{2} + 3 x^{9} y^{3} + 2 x^{9} y^{2} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + 2 x^{10} y^{4} + x^{11} y^{2} + 3 x^{10} y^{3} + x^{10} y^{2} + 3 x^{9} y^{3} + 2 x^{9} y^{2} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + x^{11} y^{4} + 4 x^{11} y^{3} + 2 x^{10} y^{4} + 3 x^{10} y^{3} + x^{10} y^{2} + 3 x^{9} y^{3} + 2 x^{9} y^{2} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 4 x^{11} y^{3} + 2 x^{10} y^{4} + x^{11} y^{2} + 4 x^{10} y^{3} + 3 x^{9} y^{3} + 2 x^{9} y^{2} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 5 x^{11} y^{3} + 2 x^{10} y^{4} + 4 x^{10} y^{3} + 3 x^{9} y^{3} + 2 x^{9} y^{2} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + x^{10} y^{4} + x^{11} y^{2} + 3 x^{10} y^{3} + 2 x^{10} y^{2} + 4 x^{9} y^{3} + x^{9} y^{2} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 2 x^{11} y^{4} + 3 x^{11} y^{3} + x^{10} y^{4} + 3 x^{10} y^{3} + 2 x^{10} y^{2} + 4 x^{9} y^{3} + x^{9} y^{2} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + x^{10} y^{4} + x^{11} y^{2} + 4 x^{10} y^{3} + x^{10} y^{2} + 4 x^{9} y^{3} + x^{9} y^{2} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + x^{11} y^{4} + 4 x^{11} y^{3} + x^{10} y^{4} + 4 x^{10} y^{3} + x^{10} y^{2} + 4 x^{9} y^{3} + x^{9} y^{2} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 4 x^{11} y^{3} + x^{10} y^{4} + x^{11} y^{2} + 5 x^{10} y^{3} + 4 x^{9} y^{3} + x^{9} y^{2} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 5 x^{11} y^{3} + x^{10} y^{4} + 5 x^{10} y^{3} + 4 x^{9} y^{3} + x^{9} y^{2} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 2 x^{11} y^{4} + 2 x^{11} y^{3} + x^{11} y^{2} + 4 x^{10} y^{3} + 2 x^{10} y^{2} + 5 x^{9} y^{3} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 2 x^{11} y^{4} + 3 x^{11} y^{3} + 4 x^{10} y^{3} + 2 x^{10} y^{2} + 5 x^{9} y^{3} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + x^{11} y^{4} + 3 x^{11} y^{3} + x^{11} y^{2} + 5 x^{10} y^{3} + x^{10} y^{2} + 5 x^{9} y^{3} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + x^{11} y^{4} + 4 x^{11} y^{3} + 5 x^{10} y^{3} + x^{10} y^{2} + 5 x^{9} y^{3} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 3 x^{12} y^{4} + 2 x^{12} y^{3} + 4 x^{11} y^{3} + x^{11} y^{2} + 6 x^{10} y^{3} + 5 x^{9} y^{3} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{4} + x^{19} y^{4} + 2 x^{18} y^{4} + 2 x^{17} y^{4} + 3 x^{16} y^{4} + 3 x^{15} y^{4} + 4 x^{14} y^{4} + 3 x^{13} y^{4} + x^{13} y^{3} + 2 x^{12} y^{4} + 3 x^{12} y^{3} + 5 x^{11} y^{3} + 6 x^{10} y^{3} + 5 x^{9} y^{3} + 4 x^{8} y^{3} + x^{8} y^{2} + 3 x^{7} y^{3} + x^{7} y^{2} + 2 x^{6} y^{3} + 2 x^{6} y^{2} + x^{5} y^{3} + 2 x^{5} y^{2} + 3 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ Here are the corresponding generator grids to these 72 possibilities:
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 2 2 2 2 2 2 1 2 2 1 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 2 2 3 3 3 2 2 2 2 1 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 1 3 3 3 2 2 1 3 3 3 1 1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 1 4 4 4 4 2 2 3 3 3 1 1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 4 4 4 4 2 2 1 4 4 4 4 1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 5 5 5 5 5 2 2 4 4 4 4 1 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 2 2 2 2 1 1 3 3 3 1 2 2 3 3 3 1 1 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 2 2 3 3 3 1 3 3 3 1 2 2 3 3 3 1 1 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 1 3 3 3 1 1 4 4 4 4 1 1 3 3 3 1 1 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 1 4 4 4 4 1 4 4 4 4 1 1 3 3 3 1 1 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 4 4 4 4 1 1 5 5 5 5 5 1 3 3 3 1 1 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 5 5 5 5 5 1 5 5 5 5 5 1 3 3 3 1 1 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 2 2 2 2 1 4 4 4 4 1 2 2 4 4 4 4 1 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 2 2 3 3 3 4 4 4 4 1 2 2 4 4 4 4 1 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 1 3 3 3 1 5 5 5 5 5 1 1 4 4 4 4 1 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 1 4 4 4 4 5 5 5 5 5 1 1 4 4 4 4 1 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 4 4 4 4 1 6 6 6 6 6 6 1 4 4 4 4 1 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 5 5 5 5 5 6 6 6 6 6 6 1 4 4 4 4 1 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 2 2 2 2 2 2 1 2 2 2 2 3 3 3 1 2 2 3 3 3 1 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 2 2 3 3 3 2 2 2 2 2 2 3 3 3 1 2 2 3 3 3 1 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 1 3 3 3 2 2 1 3 3 3 1 3 3 3 1 2 2 3 3 3 1 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 1 4 4 4 4 2 2 3 3 3 1 3 3 3 1 2 2 3 3 3 1 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 4 4 4 4 2 2 1 4 4 4 4 3 3 3 1 2 2 3 3 3 1 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 5 5 5 5 5 2 2 4 4 4 4 3 3 3 1 2 2 3 3 3 1 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 2 2 2 2 1 1 3 3 3 2 2 4 4 4 4 1 1 3 3 3 1 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 2 2 3 3 3 1 3 3 3 2 2 4 4 4 4 1 1 3 3 3 1 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 1 3 3 3 1 1 4 4 4 4 1 4 4 4 4 1 1 3 3 3 1 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 1 4 4 4 4 1 4 4 4 4 1 4 4 4 4 1 1 3 3 3 1 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 4 4 4 4 1 1 5 5 5 5 5 4 4 4 4 1 1 3 3 3 1 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 5 5 5 5 5 1 5 5 5 5 5 4 4 4 4 1 1 3 3 3 1 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 2 2 2 2 1 4 4 4 4 2 2 5 5 5 5 5 1 3 3 3 1 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 2 2 3 3 3 4 4 4 4 2 2 5 5 5 5 5 1 3 3 3 1 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 1 3 3 3 1 5 5 5 5 5 1 5 5 5 5 5 1 3 3 3 1 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 1 4 4 4 4 5 5 5 5 5 1 5 5 5 5 5 1 3 3 3 1 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 4 4 4 4 1 6 6 6 6 6 6 5 5 5 5 5 1 3 3 3 1 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 5 5 5 5 5 6 6 6 6 6 6 5 5 5 5 5 1 3 3 3 1 2 2 2 2 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 2 2 2 2 2 2 1 2 2 1 2 2 2 2 2 2 3 3 3 2 2 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 2 2 3 3 3 2 2 2 2 1 2 2 2 2 2 2 3 3 3 2 2 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 1 3 3 3 2 2 1 3 3 3 1 1 2 2 2 2 3 3 3 2 2 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 1 4 4 4 4 2 2 3 3 3 1 1 2 2 2 2 3 3 3 2 2 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 4 4 4 4 2 2 1 4 4 4 4 1 2 2 2 2 3 3 3 2 2 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 5 5 5 5 5 2 2 4 4 4 4 1 2 2 2 2 3 3 3 2 2 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 2 2 2 2 1 1 3 3 3 1 2 2 3 3 3 1 3 3 3 2 2 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 2 2 3 3 3 1 3 3 3 1 2 2 3 3 3 1 3 3 3 2 2 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 1 3 3 3 1 1 4 4 4 4 1 1 3 3 3 1 3 3 3 2 2 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 1 4 4 4 4 1 4 4 4 4 1 1 3 3 3 1 3 3 3 2 2 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 4 4 4 4 1 1 5 5 5 5 5 1 3 3 3 1 3 3 3 2 2 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 5 5 5 5 5 1 5 5 5 5 5 1 3 3 3 1 3 3 3 2 2 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 2 2 2 2 1 4 4 4 4 1 2 2 4 4 4 4 3 3 3 2 2 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 2 2 3 3 3 4 4 4 4 1 2 2 4 4 4 4 3 3 3 2 2 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 1 3 3 3 1 5 5 5 5 5 1 1 4 4 4 4 3 3 3 2 2 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 1 4 4 4 4 5 5 5 5 5 1 1 4 4 4 4 3 3 3 2 2 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 4 4 4 4 1 6 6 6 6 6 6 1 4 4 4 4 3 3 3 2 2 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 5 5 5 5 5 6 6 6 6 6 6 1 4 4 4 4 3 3 3 2 2 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 2 2 2 2 2 2 1 2 2 2 2 3 3 3 2 2 4 4 4 4 1 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 2 2 3 3 3 2 2 2 2 2 2 3 3 3 2 2 4 4 4 4 1 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 1 3 3 3 2 2 1 3 3 3 1 3 3 3 2 2 4 4 4 4 1 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 1 4 4 4 4 2 2 3 3 3 1 3 3 3 2 2 4 4 4 4 1 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 4 4 4 4 2 2 1 4 4 4 4 3 3 3 2 2 4 4 4 4 1 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 5 5 5 5 5 2 2 4 4 4 4 3 3 3 2 2 4 4 4 4 1 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 2 2 2 2 1 1 3 3 3 2 2 4 4 4 4 1 4 4 4 4 1 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 2 2 3 3 3 1 3 3 3 2 2 4 4 4 4 1 4 4 4 4 1 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 1 3 3 3 1 1 4 4 4 4 1 4 4 4 4 1 4 4 4 4 1 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 1 4 4 4 4 1 4 4 4 4 1 4 4 4 4 1 4 4 4 4 1 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 4 4 4 4 1 1 5 5 5 5 5 4 4 4 4 1 4 4 4 4 1 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 5 5 5 5 5 1 5 5 5 5 5 4 4 4 4 1 4 4 4 4 1 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 2 2 2 2 1 4 4 4 4 2 2 5 5 5 5 5 4 4 4 4 1 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 2 2 3 3 3 4 4 4 4 2 2 5 5 5 5 5 4 4 4 4 1 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 1 3 3 3 1 5 5 5 5 5 1 5 5 5 5 5 4 4 4 4 1 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 1 4 4 4 4 5 5 5 5 5 1 5 5 5 5 5 4 4 4 4 1 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 3 3 3 2 2 4 4 4 4 1 6 6 6 6 6 6 5 5 5 5 5 4 4 4 4 1 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 3 3 3 1 2 2 3 3 3 5 5 5 5 5 6 6 6 6 6 6 5 5 5 5 5 4 4 4 4 1 3 3 3 1 2 2 2 2 1 2 2 3 3 3 2 2 1 1 1 1





The AutoKron can't determine the cohomology of $\text{Gr}_2(\mathbb{R}^{12,4})$.

There are 96 possibilities.
Here are their Poincaré polynomials: $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + x^{13} y^{7} + 2 x^{13} y^{6} + x^{13} y^{5} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + 2 x^{11} y^{6} + 2 x^{11} y^{5} + x^{10} y^{6} + x^{11} y^{4} + 3 x^{10} y^{5} + 2 x^{10} y^{4} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + x^{13} y^{7} + 2 x^{13} y^{6} + x^{13} y^{5} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + 2 x^{11} y^{6} + 2 x^{11} y^{5} + x^{10} y^{6} + x^{11} y^{4} + 3 x^{10} y^{5} + 2 x^{10} y^{4} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + x^{14} y^{7} + 3 x^{14} y^{6} + x^{13} y^{7} + 3 x^{13} y^{6} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + 2 x^{11} y^{6} + 2 x^{11} y^{5} + x^{10} y^{6} + x^{11} y^{4} + 3 x^{10} y^{5} + 2 x^{10} y^{4} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + x^{14} y^{7} + 3 x^{14} y^{6} + x^{13} y^{7} + 3 x^{13} y^{6} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + 2 x^{11} y^{6} + 2 x^{11} y^{5} + x^{10} y^{6} + x^{11} y^{4} + 3 x^{10} y^{5} + 2 x^{10} y^{4} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + 3 x^{13} y^{6} + x^{13} y^{5} + 4 x^{12} y^{6} + x^{12} y^{5} + 2 x^{11} y^{6} + 2 x^{11} y^{5} + x^{10} y^{6} + x^{11} y^{4} + 3 x^{10} y^{5} + 2 x^{10} y^{4} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + 3 x^{13} y^{6} + x^{13} y^{5} + 4 x^{12} y^{6} + x^{12} y^{5} + 2 x^{11} y^{6} + 2 x^{11} y^{5} + x^{10} y^{6} + x^{11} y^{4} + 3 x^{10} y^{5} + 2 x^{10} y^{4} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + x^{14} y^{7} + 3 x^{14} y^{6} + 4 x^{13} y^{6} + 4 x^{12} y^{6} + x^{12} y^{5} + 2 x^{11} y^{6} + 2 x^{11} y^{5} + x^{10} y^{6} + x^{11} y^{4} + 3 x^{10} y^{5} + 2 x^{10} y^{4} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + x^{14} y^{7} + 3 x^{14} y^{6} + 4 x^{13} y^{6} + 4 x^{12} y^{6} + x^{12} y^{5} + 2 x^{11} y^{6} + 2 x^{11} y^{5} + x^{10} y^{6} + x^{11} y^{4} + 3 x^{10} y^{5} + 2 x^{10} y^{4} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + x^{13} y^{7} + 2 x^{13} y^{6} + x^{13} y^{5} + 2 x^{12} y^{6} + 3 x^{12} y^{5} + 2 x^{11} y^{6} + 3 x^{11} y^{5} + x^{10} y^{6} + 3 x^{10} y^{5} + 2 x^{10} y^{4} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + x^{13} y^{7} + 2 x^{13} y^{6} + x^{13} y^{5} + 2 x^{12} y^{6} + 3 x^{12} y^{5} + 2 x^{11} y^{6} + 3 x^{11} y^{5} + x^{10} y^{6} + 3 x^{10} y^{5} + 2 x^{10} y^{4} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + x^{14} y^{7} + 3 x^{14} y^{6} + x^{13} y^{7} + 3 x^{13} y^{6} + 2 x^{12} y^{6} + 3 x^{12} y^{5} + 2 x^{11} y^{6} + 3 x^{11} y^{5} + x^{10} y^{6} + 3 x^{10} y^{5} + 2 x^{10} y^{4} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + x^{14} y^{7} + 3 x^{14} y^{6} + x^{13} y^{7} + 3 x^{13} y^{6} + 2 x^{12} y^{6} + 3 x^{12} y^{5} + 2 x^{11} y^{6} + 3 x^{11} y^{5} + x^{10} y^{6} + 3 x^{10} y^{5} + 2 x^{10} y^{4} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + 3 x^{13} y^{6} + x^{13} y^{5} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + 2 x^{11} y^{6} + 3 x^{11} y^{5} + x^{10} y^{6} + 3 x^{10} y^{5} + 2 x^{10} y^{4} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + 3 x^{13} y^{6} + x^{13} y^{5} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + 2 x^{11} y^{6} + 3 x^{11} y^{5} + x^{10} y^{6} + 3 x^{10} y^{5} + 2 x^{10} y^{4} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + x^{14} y^{7} + 3 x^{14} y^{6} + 4 x^{13} y^{6} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + 2 x^{11} y^{6} + 3 x^{11} y^{5} + x^{10} y^{6} + 3 x^{10} y^{5} + 2 x^{10} y^{4} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + x^{14} y^{7} + 3 x^{14} y^{6} + 4 x^{13} y^{6} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + 2 x^{11} y^{6} + 3 x^{11} y^{5} + x^{10} y^{6} + 3 x^{10} y^{5} + 2 x^{10} y^{4} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + x^{13} y^{7} + 2 x^{13} y^{6} + x^{13} y^{5} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + x^{11} y^{6} + 3 x^{11} y^{5} + x^{10} y^{6} + x^{11} y^{4} + 4 x^{10} y^{5} + x^{10} y^{4} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + x^{13} y^{7} + 2 x^{13} y^{6} + x^{13} y^{5} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + x^{11} y^{6} + 3 x^{11} y^{5} + x^{10} y^{6} + x^{11} y^{4} + 4 x^{10} y^{5} + x^{10} y^{4} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + x^{14} y^{7} + 3 x^{14} y^{6} + x^{13} y^{7} + 3 x^{13} y^{6} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + x^{11} y^{6} + 3 x^{11} y^{5} + x^{10} y^{6} + x^{11} y^{4} + 4 x^{10} y^{5} + x^{10} y^{4} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + x^{14} y^{7} + 3 x^{14} y^{6} + x^{13} y^{7} + 3 x^{13} y^{6} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + x^{11} y^{6} + 3 x^{11} y^{5} + x^{10} y^{6} + x^{11} y^{4} + 4 x^{10} y^{5} + x^{10} y^{4} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + 3 x^{13} y^{6} + x^{13} y^{5} + 4 x^{12} y^{6} + x^{12} y^{5} + x^{11} y^{6} + 3 x^{11} y^{5} + x^{10} y^{6} + x^{11} y^{4} + 4 x^{10} y^{5} + x^{10} y^{4} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + 3 x^{13} y^{6} + x^{13} y^{5} + 4 x^{12} y^{6} + x^{12} y^{5} + x^{11} y^{6} + 3 x^{11} y^{5} + x^{10} y^{6} + x^{11} y^{4} + 4 x^{10} y^{5} + x^{10} y^{4} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + x^{14} y^{7} + 3 x^{14} y^{6} + 4 x^{13} y^{6} + 4 x^{12} y^{6} + x^{12} y^{5} + x^{11} y^{6} + 3 x^{11} y^{5} + x^{10} y^{6} + x^{11} y^{4} + 4 x^{10} y^{5} + x^{10} y^{4} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + x^{14} y^{7} + 3 x^{14} y^{6} + 4 x^{13} y^{6} + 4 x^{12} y^{6} + x^{12} y^{5} + x^{11} y^{6} + 3 x^{11} y^{5} + x^{10} y^{6} + x^{11} y^{4} + 4 x^{10} y^{5} + x^{10} y^{4} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + x^{13} y^{7} + 2 x^{13} y^{6} + x^{13} y^{5} + 2 x^{12} y^{6} + 3 x^{12} y^{5} + x^{11} y^{6} + 4 x^{11} y^{5} + x^{10} y^{6} + 4 x^{10} y^{5} + x^{10} y^{4} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + x^{13} y^{7} + 2 x^{13} y^{6} + x^{13} y^{5} + 2 x^{12} y^{6} + 3 x^{12} y^{5} + x^{11} y^{6} + 4 x^{11} y^{5} + x^{10} y^{6} + 4 x^{10} y^{5} + x^{10} y^{4} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + x^{14} y^{7} + 3 x^{14} y^{6} + x^{13} y^{7} + 3 x^{13} y^{6} + 2 x^{12} y^{6} + 3 x^{12} y^{5} + x^{11} y^{6} + 4 x^{11} y^{5} + x^{10} y^{6} + 4 x^{10} y^{5} + x^{10} y^{4} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + x^{14} y^{7} + 3 x^{14} y^{6} + x^{13} y^{7} + 3 x^{13} y^{6} + 2 x^{12} y^{6} + 3 x^{12} y^{5} + x^{11} y^{6} + 4 x^{11} y^{5} + x^{10} y^{6} + 4 x^{10} y^{5} + x^{10} y^{4} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + 3 x^{13} y^{6} + x^{13} y^{5} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + x^{11} y^{6} + 4 x^{11} y^{5} + x^{10} y^{6} + 4 x^{10} y^{5} + x^{10} y^{4} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + 3 x^{13} y^{6} + x^{13} y^{5} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + x^{11} y^{6} + 4 x^{11} y^{5} + x^{10} y^{6} + 4 x^{10} y^{5} + x^{10} y^{4} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + x^{14} y^{7} + 3 x^{14} y^{6} + 4 x^{13} y^{6} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + x^{11} y^{6} + 4 x^{11} y^{5} + x^{10} y^{6} + 4 x^{10} y^{5} + x^{10} y^{4} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + x^{14} y^{7} + 3 x^{14} y^{6} + 4 x^{13} y^{6} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + x^{11} y^{6} + 4 x^{11} y^{5} + x^{10} y^{6} + 4 x^{10} y^{5} + x^{10} y^{4} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + x^{13} y^{7} + 2 x^{13} y^{6} + x^{13} y^{5} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + 4 x^{11} y^{5} + x^{10} y^{6} + x^{11} y^{4} + 5 x^{10} y^{5} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + x^{13} y^{7} + 2 x^{13} y^{6} + x^{13} y^{5} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + 4 x^{11} y^{5} + x^{10} y^{6} + x^{11} y^{4} + 5 x^{10} y^{5} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + x^{14} y^{7} + 3 x^{14} y^{6} + x^{13} y^{7} + 3 x^{13} y^{6} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + 4 x^{11} y^{5} + x^{10} y^{6} + x^{11} y^{4} + 5 x^{10} y^{5} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + x^{14} y^{7} + 3 x^{14} y^{6} + x^{13} y^{7} + 3 x^{13} y^{6} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + 4 x^{11} y^{5} + x^{10} y^{6} + x^{11} y^{4} + 5 x^{10} y^{5} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + 3 x^{13} y^{6} + x^{13} y^{5} + 4 x^{12} y^{6} + x^{12} y^{5} + 4 x^{11} y^{5} + x^{10} y^{6} + x^{11} y^{4} + 5 x^{10} y^{5} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + 3 x^{13} y^{6} + x^{13} y^{5} + 4 x^{12} y^{6} + x^{12} y^{5} + 4 x^{11} y^{5} + x^{10} y^{6} + x^{11} y^{4} + 5 x^{10} y^{5} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + x^{14} y^{7} + 3 x^{14} y^{6} + 4 x^{13} y^{6} + 4 x^{12} y^{6} + x^{12} y^{5} + 4 x^{11} y^{5} + x^{10} y^{6} + x^{11} y^{4} + 5 x^{10} y^{5} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + x^{14} y^{7} + 3 x^{14} y^{6} + 4 x^{13} y^{6} + 4 x^{12} y^{6} + x^{12} y^{5} + 4 x^{11} y^{5} + x^{10} y^{6} + x^{11} y^{4} + 5 x^{10} y^{5} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + x^{13} y^{7} + 2 x^{13} y^{6} + x^{13} y^{5} + 2 x^{12} y^{6} + 3 x^{12} y^{5} + 5 x^{11} y^{5} + x^{10} y^{6} + 5 x^{10} y^{5} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + x^{13} y^{7} + 2 x^{13} y^{6} + x^{13} y^{5} + 2 x^{12} y^{6} + 3 x^{12} y^{5} + 5 x^{11} y^{5} + x^{10} y^{6} + 5 x^{10} y^{5} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + x^{14} y^{7} + 3 x^{14} y^{6} + x^{13} y^{7} + 3 x^{13} y^{6} + 2 x^{12} y^{6} + 3 x^{12} y^{5} + 5 x^{11} y^{5} + x^{10} y^{6} + 5 x^{10} y^{5} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + x^{14} y^{7} + 3 x^{14} y^{6} + x^{13} y^{7} + 3 x^{13} y^{6} + 2 x^{12} y^{6} + 3 x^{12} y^{5} + 5 x^{11} y^{5} + x^{10} y^{6} + 5 x^{10} y^{5} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + 3 x^{13} y^{6} + x^{13} y^{5} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + 5 x^{11} y^{5} + x^{10} y^{6} + 5 x^{10} y^{5} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + 3 x^{13} y^{6} + x^{13} y^{5} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + 5 x^{11} y^{5} + x^{10} y^{6} + 5 x^{10} y^{5} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + x^{14} y^{7} + 3 x^{14} y^{6} + 4 x^{13} y^{6} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + 5 x^{11} y^{5} + x^{10} y^{6} + 5 x^{10} y^{5} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + x^{14} y^{7} + 3 x^{14} y^{6} + 4 x^{13} y^{6} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + 5 x^{11} y^{5} + x^{10} y^{6} + 5 x^{10} y^{5} + 3 x^{9} y^{5} + 2 x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + x^{13} y^{7} + 2 x^{13} y^{6} + x^{13} y^{5} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + 2 x^{11} y^{6} + 2 x^{11} y^{5} + x^{11} y^{4} + 4 x^{10} y^{5} + 2 x^{10} y^{4} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + x^{13} y^{7} + 2 x^{13} y^{6} + x^{13} y^{5} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + 2 x^{11} y^{6} + 2 x^{11} y^{5} + x^{11} y^{4} + 4 x^{10} y^{5} + 2 x^{10} y^{4} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + x^{14} y^{7} + 3 x^{14} y^{6} + x^{13} y^{7} + 3 x^{13} y^{6} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + 2 x^{11} y^{6} + 2 x^{11} y^{5} + x^{11} y^{4} + 4 x^{10} y^{5} + 2 x^{10} y^{4} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + x^{14} y^{7} + 3 x^{14} y^{6} + x^{13} y^{7} + 3 x^{13} y^{6} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + 2 x^{11} y^{6} + 2 x^{11} y^{5} + x^{11} y^{4} + 4 x^{10} y^{5} + 2 x^{10} y^{4} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + 3 x^{13} y^{6} + x^{13} y^{5} + 4 x^{12} y^{6} + x^{12} y^{5} + 2 x^{11} y^{6} + 2 x^{11} y^{5} + x^{11} y^{4} + 4 x^{10} y^{5} + 2 x^{10} y^{4} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + 3 x^{13} y^{6} + x^{13} y^{5} + 4 x^{12} y^{6} + x^{12} y^{5} + 2 x^{11} y^{6} + 2 x^{11} y^{5} + x^{11} y^{4} + 4 x^{10} y^{5} + 2 x^{10} y^{4} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + x^{14} y^{7} + 3 x^{14} y^{6} + 4 x^{13} y^{6} + 4 x^{12} y^{6} + x^{12} y^{5} + 2 x^{11} y^{6} + 2 x^{11} y^{5} + x^{11} y^{4} + 4 x^{10} y^{5} + 2 x^{10} y^{4} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + x^{14} y^{7} + 3 x^{14} y^{6} + 4 x^{13} y^{6} + 4 x^{12} y^{6} + x^{12} y^{5} + 2 x^{11} y^{6} + 2 x^{11} y^{5} + x^{11} y^{4} + 4 x^{10} y^{5} + 2 x^{10} y^{4} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + x^{13} y^{7} + 2 x^{13} y^{6} + x^{13} y^{5} + 2 x^{12} y^{6} + 3 x^{12} y^{5} + 2 x^{11} y^{6} + 3 x^{11} y^{5} + 4 x^{10} y^{5} + 2 x^{10} y^{4} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + x^{13} y^{7} + 2 x^{13} y^{6} + x^{13} y^{5} + 2 x^{12} y^{6} + 3 x^{12} y^{5} + 2 x^{11} y^{6} + 3 x^{11} y^{5} + 4 x^{10} y^{5} + 2 x^{10} y^{4} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + x^{14} y^{7} + 3 x^{14} y^{6} + x^{13} y^{7} + 3 x^{13} y^{6} + 2 x^{12} y^{6} + 3 x^{12} y^{5} + 2 x^{11} y^{6} + 3 x^{11} y^{5} + 4 x^{10} y^{5} + 2 x^{10} y^{4} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + x^{14} y^{7} + 3 x^{14} y^{6} + x^{13} y^{7} + 3 x^{13} y^{6} + 2 x^{12} y^{6} + 3 x^{12} y^{5} + 2 x^{11} y^{6} + 3 x^{11} y^{5} + 4 x^{10} y^{5} + 2 x^{10} y^{4} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + 3 x^{13} y^{6} + x^{13} y^{5} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + 2 x^{11} y^{6} + 3 x^{11} y^{5} + 4 x^{10} y^{5} + 2 x^{10} y^{4} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + 3 x^{13} y^{6} + x^{13} y^{5} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + 2 x^{11} y^{6} + 3 x^{11} y^{5} + 4 x^{10} y^{5} + 2 x^{10} y^{4} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + x^{14} y^{7} + 3 x^{14} y^{6} + 4 x^{13} y^{6} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + 2 x^{11} y^{6} + 3 x^{11} y^{5} + 4 x^{10} y^{5} + 2 x^{10} y^{4} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + x^{14} y^{7} + 3 x^{14} y^{6} + 4 x^{13} y^{6} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + 2 x^{11} y^{6} + 3 x^{11} y^{5} + 4 x^{10} y^{5} + 2 x^{10} y^{4} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + x^{13} y^{7} + 2 x^{13} y^{6} + x^{13} y^{5} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + x^{11} y^{6} + 3 x^{11} y^{5} + x^{11} y^{4} + 5 x^{10} y^{5} + x^{10} y^{4} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + x^{13} y^{7} + 2 x^{13} y^{6} + x^{13} y^{5} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + x^{11} y^{6} + 3 x^{11} y^{5} + x^{11} y^{4} + 5 x^{10} y^{5} + x^{10} y^{4} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + x^{14} y^{7} + 3 x^{14} y^{6} + x^{13} y^{7} + 3 x^{13} y^{6} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + x^{11} y^{6} + 3 x^{11} y^{5} + x^{11} y^{4} + 5 x^{10} y^{5} + x^{10} y^{4} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + x^{14} y^{7} + 3 x^{14} y^{6} + x^{13} y^{7} + 3 x^{13} y^{6} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + x^{11} y^{6} + 3 x^{11} y^{5} + x^{11} y^{4} + 5 x^{10} y^{5} + x^{10} y^{4} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + 3 x^{13} y^{6} + x^{13} y^{5} + 4 x^{12} y^{6} + x^{12} y^{5} + x^{11} y^{6} + 3 x^{11} y^{5} + x^{11} y^{4} + 5 x^{10} y^{5} + x^{10} y^{4} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + 3 x^{13} y^{6} + x^{13} y^{5} + 4 x^{12} y^{6} + x^{12} y^{5} + x^{11} y^{6} + 3 x^{11} y^{5} + x^{11} y^{4} + 5 x^{10} y^{5} + x^{10} y^{4} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + x^{14} y^{7} + 3 x^{14} y^{6} + 4 x^{13} y^{6} + 4 x^{12} y^{6} + x^{12} y^{5} + x^{11} y^{6} + 3 x^{11} y^{5} + x^{11} y^{4} + 5 x^{10} y^{5} + x^{10} y^{4} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + x^{14} y^{7} + 3 x^{14} y^{6} + 4 x^{13} y^{6} + 4 x^{12} y^{6} + x^{12} y^{5} + x^{11} y^{6} + 3 x^{11} y^{5} + x^{11} y^{4} + 5 x^{10} y^{5} + x^{10} y^{4} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + x^{13} y^{7} + 2 x^{13} y^{6} + x^{13} y^{5} + 2 x^{12} y^{6} + 3 x^{12} y^{5} + x^{11} y^{6} + 4 x^{11} y^{5} + 5 x^{10} y^{5} + x^{10} y^{4} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + x^{13} y^{7} + 2 x^{13} y^{6} + x^{13} y^{5} + 2 x^{12} y^{6} + 3 x^{12} y^{5} + x^{11} y^{6} + 4 x^{11} y^{5} + 5 x^{10} y^{5} + x^{10} y^{4} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + x^{14} y^{7} + 3 x^{14} y^{6} + x^{13} y^{7} + 3 x^{13} y^{6} + 2 x^{12} y^{6} + 3 x^{12} y^{5} + x^{11} y^{6} + 4 x^{11} y^{5} + 5 x^{10} y^{5} + x^{10} y^{4} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + x^{14} y^{7} + 3 x^{14} y^{6} + x^{13} y^{7} + 3 x^{13} y^{6} + 2 x^{12} y^{6} + 3 x^{12} y^{5} + x^{11} y^{6} + 4 x^{11} y^{5} + 5 x^{10} y^{5} + x^{10} y^{4} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + 3 x^{13} y^{6} + x^{13} y^{5} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + x^{11} y^{6} + 4 x^{11} y^{5} + 5 x^{10} y^{5} + x^{10} y^{4} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + 3 x^{13} y^{6} + x^{13} y^{5} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + x^{11} y^{6} + 4 x^{11} y^{5} + 5 x^{10} y^{5} + x^{10} y^{4} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + x^{14} y^{7} + 3 x^{14} y^{6} + 4 x^{13} y^{6} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + x^{11} y^{6} + 4 x^{11} y^{5} + 5 x^{10} y^{5} + x^{10} y^{4} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + x^{14} y^{7} + 3 x^{14} y^{6} + 4 x^{13} y^{6} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + x^{11} y^{6} + 4 x^{11} y^{5} + 5 x^{10} y^{5} + x^{10} y^{4} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + x^{13} y^{7} + 2 x^{13} y^{6} + x^{13} y^{5} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + 4 x^{11} y^{5} + x^{11} y^{4} + 6 x^{10} y^{5} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + x^{13} y^{7} + 2 x^{13} y^{6} + x^{13} y^{5} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + 4 x^{11} y^{5} + x^{11} y^{4} + 6 x^{10} y^{5} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + x^{14} y^{7} + 3 x^{14} y^{6} + x^{13} y^{7} + 3 x^{13} y^{6} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + 4 x^{11} y^{5} + x^{11} y^{4} + 6 x^{10} y^{5} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + x^{14} y^{7} + 3 x^{14} y^{6} + x^{13} y^{7} + 3 x^{13} y^{6} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + 4 x^{11} y^{5} + x^{11} y^{4} + 6 x^{10} y^{5} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + 3 x^{13} y^{6} + x^{13} y^{5} + 4 x^{12} y^{6} + x^{12} y^{5} + 4 x^{11} y^{5} + x^{11} y^{4} + 6 x^{10} y^{5} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + 3 x^{13} y^{6} + x^{13} y^{5} + 4 x^{12} y^{6} + x^{12} y^{5} + 4 x^{11} y^{5} + x^{11} y^{4} + 6 x^{10} y^{5} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + x^{14} y^{7} + 3 x^{14} y^{6} + 4 x^{13} y^{6} + 4 x^{12} y^{6} + x^{12} y^{5} + 4 x^{11} y^{5} + x^{11} y^{4} + 6 x^{10} y^{5} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + x^{14} y^{7} + 3 x^{14} y^{6} + 4 x^{13} y^{6} + 4 x^{12} y^{6} + x^{12} y^{5} + 4 x^{11} y^{5} + x^{11} y^{4} + 6 x^{10} y^{5} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + x^{13} y^{7} + 2 x^{13} y^{6} + x^{13} y^{5} + 2 x^{12} y^{6} + 3 x^{12} y^{5} + 5 x^{11} y^{5} + 6 x^{10} y^{5} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + x^{13} y^{7} + 2 x^{13} y^{6} + x^{13} y^{5} + 2 x^{12} y^{6} + 3 x^{12} y^{5} + 5 x^{11} y^{5} + 6 x^{10} y^{5} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + x^{14} y^{7} + 3 x^{14} y^{6} + x^{13} y^{7} + 3 x^{13} y^{6} + 2 x^{12} y^{6} + 3 x^{12} y^{5} + 5 x^{11} y^{5} + 6 x^{10} y^{5} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + x^{14} y^{7} + 3 x^{14} y^{6} + x^{13} y^{7} + 3 x^{13} y^{6} + 2 x^{12} y^{6} + 3 x^{12} y^{5} + 5 x^{11} y^{5} + 6 x^{10} y^{5} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + 3 x^{13} y^{6} + x^{13} y^{5} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + 5 x^{11} y^{5} + 6 x^{10} y^{5} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + 2 x^{14} y^{7} + 2 x^{14} y^{6} + 3 x^{13} y^{6} + x^{13} y^{5} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + 5 x^{11} y^{5} + 6 x^{10} y^{5} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + x^{16} y^{8} + 2 x^{16} y^{7} + 2 x^{15} y^{7} + x^{15} y^{6} + x^{14} y^{7} + 3 x^{14} y^{6} + 4 x^{13} y^{6} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + 5 x^{11} y^{5} + 6 x^{10} y^{5} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{8} + x^{19} y^{8} + 2 x^{18} y^{8} + x^{17} y^{8} + x^{17} y^{7} + 3 x^{16} y^{7} + 3 x^{15} y^{7} + x^{14} y^{7} + 3 x^{14} y^{6} + 4 x^{13} y^{6} + 3 x^{12} y^{6} + 2 x^{12} y^{5} + 5 x^{11} y^{5} + 6 x^{10} y^{5} + 4 x^{9} y^{5} + x^{9} y^{4} + x^{8} y^{5} + 4 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ Here are the corresponding generator grids to these 96 possibilities:
1 1 2 2 1 1 1 2 2 2 2 1 2 2 2 2 1 2 2 1 3 3 3 2 2 2 2 2 2 1 1 3 3 3 2 2 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 2 2 2 2 1 2 2 1 3 3 3 2 2 2 2 2 2 1 1 3 3 3 2 2 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 1 3 3 3 1 3 3 3 3 3 3 2 2 2 2 2 2 1 1 3 3 3 2 2 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 1 3 3 3 1 3 3 3 3 3 3 2 2 2 2 2 2 1 1 3 3 3 2 2 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 2 2 2 2 3 3 3 1 4 4 4 4 1 2 2 2 2 1 1 3 3 3 2 2 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 2 2 2 2 3 3 3 1 4 4 4 4 1 2 2 2 2 1 1 3 3 3 2 2 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 1 3 3 3 4 4 4 4 4 4 4 4 1 2 2 2 2 1 1 3 3 3 2 2 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 1 3 3 3 4 4 4 4 4 4 4 4 1 2 2 2 2 1 1 3 3 3 2 2 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 2 2 2 2 1 2 2 1 2 2 3 3 3 2 2 3 3 3 1 3 3 3 2 2 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 2 2 2 2 1 2 2 1 2 2 3 3 3 2 2 3 3 3 1 3 3 3 2 2 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 1 3 3 3 1 3 3 3 2 2 3 3 3 2 2 3 3 3 1 3 3 3 2 2 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 1 3 3 3 1 3 3 3 2 2 3 3 3 2 2 3 3 3 1 3 3 3 2 2 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 2 2 2 2 3 3 3 1 3 3 3 2 2 2 2 3 3 3 1 3 3 3 2 2 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 2 2 2 2 3 3 3 1 3 3 3 2 2 2 2 3 3 3 1 3 3 3 2 2 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 1 3 3 3 4 4 4 4 3 3 3 2 2 2 2 3 3 3 1 3 3 3 2 2 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 1 3 3 3 4 4 4 4 3 3 3 2 2 2 2 3 3 3 1 3 3 3 2 2 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 2 2 2 2 1 2 2 1 3 3 3 2 2 1 3 3 3 1 1 4 4 4 4 1 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 2 2 2 2 1 2 2 1 3 3 3 2 2 1 3 3 3 1 1 4 4 4 4 1 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 1 3 3 3 1 3 3 3 3 3 3 2 2 1 3 3 3 1 1 4 4 4 4 1 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 1 3 3 3 1 3 3 3 3 3 3 2 2 1 3 3 3 1 1 4 4 4 4 1 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 2 2 2 2 3 3 3 1 4 4 4 4 1 1 3 3 3 1 1 4 4 4 4 1 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 2 2 2 2 3 3 3 1 4 4 4 4 1 1 3 3 3 1 1 4 4 4 4 1 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 1 3 3 3 4 4 4 4 4 4 4 4 1 1 3 3 3 1 1 4 4 4 4 1 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 1 3 3 3 4 4 4 4 4 4 4 4 1 1 3 3 3 1 1 4 4 4 4 1 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 2 2 2 2 1 2 2 1 2 2 3 3 3 1 4 4 4 4 1 4 4 4 4 1 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 2 2 2 2 1 2 2 1 2 2 3 3 3 1 4 4 4 4 1 4 4 4 4 1 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 1 3 3 3 1 3 3 3 2 2 3 3 3 1 4 4 4 4 1 4 4 4 4 1 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 1 3 3 3 1 3 3 3 2 2 3 3 3 1 4 4 4 4 1 4 4 4 4 1 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 2 2 2 2 3 3 3 1 3 3 3 2 2 1 4 4 4 4 1 4 4 4 4 1 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 2 2 2 2 3 3 3 1 3 3 3 2 2 1 4 4 4 4 1 4 4 4 4 1 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 1 3 3 3 4 4 4 4 3 3 3 2 2 1 4 4 4 4 1 4 4 4 4 1 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 1 3 3 3 4 4 4 4 3 3 3 2 2 1 4 4 4 4 1 4 4 4 4 1 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 2 2 2 2 1 2 2 1 3 3 3 2 2 4 4 4 4 1 1 5 5 5 5 5 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 2 2 2 2 1 2 2 1 3 3 3 2 2 4 4 4 4 1 1 5 5 5 5 5 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 1 3 3 3 1 3 3 3 3 3 3 2 2 4 4 4 4 1 1 5 5 5 5 5 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 1 3 3 3 1 3 3 3 3 3 3 2 2 4 4 4 4 1 1 5 5 5 5 5 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 2 2 2 2 3 3 3 1 4 4 4 4 1 4 4 4 4 1 1 5 5 5 5 5 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 2 2 2 2 3 3 3 1 4 4 4 4 1 4 4 4 4 1 1 5 5 5 5 5 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 1 3 3 3 4 4 4 4 4 4 4 4 1 4 4 4 4 1 1 5 5 5 5 5 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 1 3 3 3 4 4 4 4 4 4 4 4 1 4 4 4 4 1 1 5 5 5 5 5 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 2 2 2 2 1 2 2 1 2 2 3 3 3 5 5 5 5 5 1 5 5 5 5 5 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 2 2 2 2 1 2 2 1 2 2 3 3 3 5 5 5 5 5 1 5 5 5 5 5 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 1 3 3 3 1 3 3 3 2 2 3 3 3 5 5 5 5 5 1 5 5 5 5 5 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 1 3 3 3 1 3 3 3 2 2 3 3 3 5 5 5 5 5 1 5 5 5 5 5 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 2 2 2 2 3 3 3 1 3 3 3 2 2 5 5 5 5 5 1 5 5 5 5 5 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 2 2 2 2 3 3 3 1 3 3 3 2 2 5 5 5 5 5 1 5 5 5 5 5 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 1 3 3 3 4 4 4 4 3 3 3 2 2 5 5 5 5 5 1 5 5 5 5 5 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 1 3 3 3 4 4 4 4 3 3 3 2 2 5 5 5 5 5 1 5 5 5 5 5 3 3 3 2 2 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 2 2 2 2 1 2 2 1 3 3 3 2 2 2 2 2 2 1 4 4 4 4 2 2 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 2 2 2 2 1 2 2 1 3 3 3 2 2 2 2 2 2 1 4 4 4 4 2 2 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 1 3 3 3 1 3 3 3 3 3 3 2 2 2 2 2 2 1 4 4 4 4 2 2 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 1 3 3 3 1 3 3 3 3 3 3 2 2 2 2 2 2 1 4 4 4 4 2 2 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 2 2 2 2 3 3 3 1 4 4 4 4 1 2 2 2 2 1 4 4 4 4 2 2 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 2 2 2 2 3 3 3 1 4 4 4 4 1 2 2 2 2 1 4 4 4 4 2 2 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 1 3 3 3 4 4 4 4 4 4 4 4 1 2 2 2 2 1 4 4 4 4 2 2 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 1 3 3 3 4 4 4 4 4 4 4 4 1 2 2 2 2 1 4 4 4 4 2 2 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 2 2 2 2 1 2 2 1 2 2 3 3 3 2 2 3 3 3 4 4 4 4 2 2 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 2 2 2 2 1 2 2 1 2 2 3 3 3 2 2 3 3 3 4 4 4 4 2 2 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 1 3 3 3 1 3 3 3 2 2 3 3 3 2 2 3 3 3 4 4 4 4 2 2 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 1 3 3 3 1 3 3 3 2 2 3 3 3 2 2 3 3 3 4 4 4 4 2 2 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 2 2 2 2 3 3 3 1 3 3 3 2 2 2 2 3 3 3 4 4 4 4 2 2 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 2 2 2 2 3 3 3 1 3 3 3 2 2 2 2 3 3 3 4 4 4 4 2 2 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 1 3 3 3 4 4 4 4 3 3 3 2 2 2 2 3 3 3 4 4 4 4 2 2 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 1 3 3 3 4 4 4 4 3 3 3 2 2 2 2 3 3 3 4 4 4 4 2 2 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 2 2 2 2 1 2 2 1 3 3 3 2 2 1 3 3 3 1 5 5 5 5 5 1 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 2 2 2 2 1 2 2 1 3 3 3 2 2 1 3 3 3 1 5 5 5 5 5 1 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 1 3 3 3 1 3 3 3 3 3 3 2 2 1 3 3 3 1 5 5 5 5 5 1 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 1 3 3 3 1 3 3 3 3 3 3 2 2 1 3 3 3 1 5 5 5 5 5 1 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 2 2 2 2 3 3 3 1 4 4 4 4 1 1 3 3 3 1 5 5 5 5 5 1 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 2 2 2 2 3 3 3 1 4 4 4 4 1 1 3 3 3 1 5 5 5 5 5 1 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 1 3 3 3 4 4 4 4 4 4 4 4 1 1 3 3 3 1 5 5 5 5 5 1 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 1 3 3 3 4 4 4 4 4 4 4 4 1 1 3 3 3 1 5 5 5 5 5 1 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 2 2 2 2 1 2 2 1 2 2 3 3 3 1 4 4 4 4 5 5 5 5 5 1 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 2 2 2 2 1 2 2 1 2 2 3 3 3 1 4 4 4 4 5 5 5 5 5 1 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 1 3 3 3 1 3 3 3 2 2 3 3 3 1 4 4 4 4 5 5 5 5 5 1 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 1 3 3 3 1 3 3 3 2 2 3 3 3 1 4 4 4 4 5 5 5 5 5 1 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 2 2 2 2 3 3 3 1 3 3 3 2 2 1 4 4 4 4 5 5 5 5 5 1 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 2 2 2 2 3 3 3 1 3 3 3 2 2 1 4 4 4 4 5 5 5 5 5 1 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 1 3 3 3 4 4 4 4 3 3 3 2 2 1 4 4 4 4 5 5 5 5 5 1 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 1 3 3 3 4 4 4 4 3 3 3 2 2 1 4 4 4 4 5 5 5 5 5 1 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 2 2 2 2 1 2 2 1 3 3 3 2 2 4 4 4 4 1 6 6 6 6 6 6 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 2 2 2 2 1 2 2 1 3 3 3 2 2 4 4 4 4 1 6 6 6 6 6 6 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 1 3 3 3 1 3 3 3 3 3 3 2 2 4 4 4 4 1 6 6 6 6 6 6 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 1 3 3 3 1 3 3 3 3 3 3 2 2 4 4 4 4 1 6 6 6 6 6 6 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 2 2 2 2 3 3 3 1 4 4 4 4 1 4 4 4 4 1 6 6 6 6 6 6 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 2 2 2 2 3 3 3 1 4 4 4 4 1 4 4 4 4 1 6 6 6 6 6 6 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 1 3 3 3 4 4 4 4 4 4 4 4 1 4 4 4 4 1 6 6 6 6 6 6 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 1 3 3 3 4 4 4 4 4 4 4 4 1 4 4 4 4 1 6 6 6 6 6 6 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 2 2 2 2 1 2 2 1 2 2 3 3 3 5 5 5 5 5 6 6 6 6 6 6 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 2 2 2 2 1 2 2 1 2 2 3 3 3 5 5 5 5 5 6 6 6 6 6 6 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 1 3 3 3 1 3 3 3 2 2 3 3 3 5 5 5 5 5 6 6 6 6 6 6 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 1 3 3 3 1 3 3 3 2 2 3 3 3 5 5 5 5 5 6 6 6 6 6 6 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 2 2 2 2 3 3 3 1 3 3 3 2 2 5 5 5 5 5 6 6 6 6 6 6 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 2 2 2 2 3 3 3 1 3 3 3 2 2 5 5 5 5 5 6 6 6 6 6 6 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 1 2 2 2 2 1 1 3 3 3 4 4 4 4 3 3 3 2 2 5 5 5 5 5 6 6 6 6 6 6 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 3 3 3 1 3 3 3 4 4 4 4 3 3 3 2 2 5 5 5 5 5 6 6 6 6 6 6 4 4 4 4 1 1 4 4 4 4 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1





The AutoKron can't determine the cohomology of $\text{Gr}_2(\mathbb{R}^{12,5})$.

There are 4 possibilities.
Here are their Poincaré polynomials: $$x^{20} y^{10} + x^{19} y^{9} + 2 x^{18} y^{9} + x^{17} y^{9} + x^{17} y^{8} + 3 x^{16} y^{8} + 2 x^{15} y^{8} + x^{15} y^{7} + x^{14} y^{8} + 3 x^{14} y^{7} + 3 x^{13} y^{7} + x^{13} y^{6} + x^{12} y^{7} + 4 x^{12} y^{6} + 4 x^{11} y^{6} + x^{11} y^{5} + 2 x^{10} y^{6} + 4 x^{10} y^{5} + 5 x^{9} y^{5} + 2 x^{8} y^{5} + 3 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{10} + x^{19} y^{9} + 2 x^{18} y^{9} + x^{17} y^{9} + x^{17} y^{8} + 3 x^{16} y^{8} + 2 x^{15} y^{8} + x^{15} y^{7} + 4 x^{14} y^{7} + 4 x^{13} y^{7} + x^{12} y^{7} + 4 x^{12} y^{6} + 4 x^{11} y^{6} + x^{11} y^{5} + 2 x^{10} y^{6} + 4 x^{10} y^{5} + 5 x^{9} y^{5} + 2 x^{8} y^{5} + 3 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{10} + x^{19} y^{9} + 2 x^{18} y^{9} + x^{17} y^{9} + x^{17} y^{8} + 3 x^{16} y^{8} + 2 x^{15} y^{8} + x^{15} y^{7} + x^{14} y^{8} + 3 x^{14} y^{7} + 3 x^{13} y^{7} + x^{13} y^{6} + 5 x^{12} y^{6} + 5 x^{11} y^{6} + 2 x^{10} y^{6} + 4 x^{10} y^{5} + 5 x^{9} y^{5} + 2 x^{8} y^{5} + 3 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ $$x^{20} y^{10} + x^{19} y^{9} + 2 x^{18} y^{9} + x^{17} y^{9} + x^{17} y^{8} + 3 x^{16} y^{8} + 2 x^{15} y^{8} + x^{15} y^{7} + 4 x^{14} y^{7} + 4 x^{13} y^{7} + 5 x^{12} y^{6} + 5 x^{11} y^{6} + 2 x^{10} y^{6} + 4 x^{10} y^{5} + 5 x^{9} y^{5} + 2 x^{8} y^{5} + 3 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ Here are the corresponding generator grids to these 4 possibilities:
1 1 2 2 1 1 3 3 3 2 2 1 1 3 3 3 3 3 3 1 1 4 4 4 4 4 4 4 4 1 2 2 4 4 4 4 5 5 5 5 5 2 2 3 3 3 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 2 2 1 4 4 4 4 4 4 4 4 1 4 4 4 4 4 4 4 4 1 2 2 4 4 4 4 5 5 5 5 5 2 2 3 3 3 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 2 2 1 1 3 3 3 3 3 3 1 5 5 5 5 5 5 5 5 5 5 2 2 4 4 4 4 5 5 5 5 5 2 2 3 3 3 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
1 1 2 2 1 1 3 3 3 2 2 1 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 2 2 4 4 4 4 5 5 5 5 5 2 2 3 3 3 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1





The cohomology of $\text{Gr}_2(\mathbb{R}^{12,6})$

Poincaré polynomial: $$x^{20} y^{10} + x^{19} y^{10} + x^{18} y^{10} + x^{18} y^{9} + 2 x^{17} y^{9} + x^{16} y^{9} + 2 x^{16} y^{8} + 3 x^{15} y^{8} + 2 x^{14} y^{8} + 2 x^{14} y^{7} + 4 x^{13} y^{7} + 2 x^{12} y^{7} + 3 x^{12} y^{6} + 5 x^{11} y^{6} + 3 x^{10} y^{6} + 3 x^{10} y^{5} + 5 x^{9} y^{5} + 2 x^{8} y^{5} + 3 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ Generator count grid:
1 1 1 1 2 2 1 2 2 3 3 3 2 2 2 2 4 4 4 4 2 2 3 3 3 5 5 5 5 5 3 3 3 3 3 3 5 5 5 5 5 2 2 3 3 3 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
Explicitly, as a free module over the ground ring $\mathbb{M}_2$: $$H^{\ast,\ast}(\text{Gr}_2(\mathbb{R}^{12,6}))=\mathbb{M}_2\oplus\Sigma^{1,1}\mathbb{M}_2\oplus\Sigma^{2,1}\mathbb{M}_2\oplus\Sigma^{2,2}\mathbb{M}_2\oplus\Sigma^{3,2}\mathbb{M}_2\oplus\Sigma^{4,2}\mathbb{M}_2\oplus\Sigma^{4,3}\mathbb{M}_2\oplus\Sigma^{5,3}\mathbb{M}_2\oplus\Sigma^{6,3}\mathbb{M}_2\oplus\Sigma^{6,4}\mathbb{M}_2\oplus\Sigma^{7,4}\mathbb{M}_2\oplus\Sigma^{8,4}\mathbb{M}_2\oplus\Sigma^{8,5}\mathbb{M}_2\oplus\Sigma^{9,5}\mathbb{M}_2\oplus\Sigma^{10,5}\mathbb{M}_2\oplus\Sigma^{10,6}\mathbb{M}_2\oplus\Sigma^{11,6}\mathbb{M}_2\oplus\Sigma^{12,6}\mathbb{M}_2\oplus\Sigma^{12,7}\mathbb{M}_2\oplus\Sigma^{13,7}\mathbb{M}_2\oplus\Sigma^{14,7}\mathbb{M}_2\oplus\Sigma^{14,8}\mathbb{M}_2\oplus\Sigma^{15,8}\mathbb{M}_2\oplus\Sigma^{16,8}\mathbb{M}_2\oplus\Sigma^{16,9}\mathbb{M}_2\oplus\Sigma^{17,9}\mathbb{M}_2\oplus\Sigma^{18,9}\mathbb{M}_2\oplus\Sigma^{18,10}\mathbb{M}_2\oplus\Sigma^{19,10}\mathbb{M}_2\oplus\Sigma^{20,10}\mathbb{M}_2.$$




The cohomology of $\text{Gr}_2(\mathbb{R}^{13,1})$

Poincaré polynomial: $$x^{22} y^{2} + x^{21} y^{2} + 2 x^{20} y^{2} + 2 x^{19} y^{2} + 3 x^{18} y^{2} + 3 x^{17} y^{2} + 4 x^{16} y^{2} + 4 x^{15} y^{2} + 5 x^{14} y^{2} + 5 x^{13} y^{2} + 5 x^{12} y^{2} + x^{12} y + 4 x^{11} y^{2} + 2 x^{11} y + 4 x^{10} y^{2} + 2 x^{10} y + 3 x^{9} y^{2} + 2 x^{9} y + 3 x^{8} y^{2} + 2 x^{8} y + 2 x^{7} y^{2} + 2 x^{7} y + 2 x^{6} y^{2} + 2 x^{6} y + x^{5} y^{2} + 2 x^{5} y + x^{4} y^{2} + 2 x^{4} y + 2 x^{3} y + 2 x^{2} y + x y + 1$$ Generator count grid:
1 1 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 1 4 4 4 4 2 2 4 4 4 4 2 2 3 3 3 2 2 3 3 3 2 2 2 2 2 2 2 2 2 2 1 2 2 1 2 2 2 2 2 2 1 1
Explicitly, as a free module over the ground ring $\mathbb{M}_2$: $$H^{\ast,\ast}(\text{Gr}_2(\mathbb{R}^{13,1}))=\mathbb{M}_2\oplus\Sigma^{1,1}\mathbb{M}_2\oplus\Sigma^{2,1}\mathbb{M}_2\oplus\Sigma^{3,1}\mathbb{M}_2\oplus\Sigma^{4,1}\mathbb{M}_2\oplus\Sigma^{4,2}\mathbb{M}_2\oplus\Sigma^{5,1}\mathbb{M}_2\oplus\Sigma^{5,2}\mathbb{M}_2\oplus\Sigma^{6,1}\mathbb{M}_2\oplus\Sigma^{6,2}\mathbb{M}_2\oplus\Sigma^{7,1}\mathbb{M}_2\oplus\Sigma^{7,2}\mathbb{M}_2\oplus\Sigma^{8,1}\mathbb{M}_2\oplus\Sigma^{8,2}\mathbb{M}_2\oplus\Sigma^{9,1}\mathbb{M}_2\oplus\Sigma^{9,2}\mathbb{M}_2\oplus\Sigma^{10,1}\mathbb{M}_2\oplus\Sigma^{10,2}\mathbb{M}_2\oplus\Sigma^{11,1}\mathbb{M}_2\oplus\Sigma^{11,2}\mathbb{M}_2\oplus\Sigma^{12,1}\mathbb{M}_2\oplus\Sigma^{12,2}\mathbb{M}_2\oplus\Sigma^{13,2}\mathbb{M}_2\oplus\Sigma^{14,2}\mathbb{M}_2\oplus\Sigma^{15,2}\mathbb{M}_2\oplus\Sigma^{16,2}\mathbb{M}_2\oplus\Sigma^{17,2}\mathbb{M}_2\oplus\Sigma^{18,2}\mathbb{M}_2\oplus\Sigma^{19,2}\mathbb{M}_2\oplus\Sigma^{20,2}\mathbb{M}_2\oplus\Sigma^{21,2}\mathbb{M}_2\oplus\Sigma^{22,2}\mathbb{M}_2.$$




The cohomology of $\text{Gr}_2(\mathbb{R}^{13,6})$

Poincaré polynomial: $$x^{22} y^{11} + x^{21} y^{11} + 2 x^{20} y^{10} + 2 x^{19} y^{10} + x^{18} y^{10} + 2 x^{18} y^{9} + 3 x^{17} y^{9} + x^{16} y^{9} + 3 x^{16} y^{8} + 4 x^{15} y^{8} + 2 x^{14} y^{8} + 3 x^{14} y^{7} + 5 x^{13} y^{7} + 2 x^{12} y^{7} + 4 x^{12} y^{6} + 6 x^{11} y^{6} + 3 x^{10} y^{6} + 3 x^{10} y^{5} + 5 x^{9} y^{5} + 2 x^{8} y^{5} + 3 x^{8} y^{4} + 4 x^{7} y^{4} + 2 x^{6} y^{4} + 2 x^{6} y^{3} + 3 x^{5} y^{3} + x^{4} y^{3} + 2 x^{4} y^{2} + 2 x^{3} y^{2} + x^{2} y^{2} + x^{2} y + x y + 1$$ Generator count grid:
1 1 2 2 2 2 1 2 2 3 3 3 1 3 3 3 4 4 4 4 2 2 3 3 3 5 5 5 5 5 2 2 4 4 4 4 6 6 6 6 6 6 3 3 3 3 3 3 5 5 5 5 5 2 2 3 3 3 4 4 4 4 2 2 2 2 3 3 3 1 2 2 2 2 1 1 1 1
Explicitly, as a free module over the ground ring $\mathbb{M}_2$: $$H^{\ast,\ast}(\text{Gr}_2(\mathbb{R}^{13,6}))=\mathbb{M}_2\oplus\Sigma^{1,1}\mathbb{M}_2\oplus\Sigma^{2,1}\mathbb{M}_2\oplus\Sigma^{2,2}\mathbb{M}_2\oplus\Sigma^{3,2}\mathbb{M}_2\oplus\Sigma^{4,2}\mathbb{M}_2\oplus\Sigma^{4,3}\mathbb{M}_2\oplus\Sigma^{5,3}\mathbb{M}_2\oplus\Sigma^{6,3}\mathbb{M}_2\oplus\Sigma^{6,4}\mathbb{M}_2\oplus\Sigma^{7,4}\mathbb{M}_2\oplus\Sigma^{8,4}\mathbb{M}_2\oplus\Sigma^{8,5}\mathbb{M}_2\oplus\Sigma^{9,5}\mathbb{M}_2\oplus\Sigma^{10,5}\mathbb{M}_2\oplus\Sigma^{10,6}\mathbb{M}_2\oplus\Sigma^{11,6}\mathbb{M}_2\oplus\Sigma^{12,6}\mathbb{M}_2\oplus\Sigma^{12,7}\mathbb{M}_2\oplus\Sigma^{13,7}\mathbb{M}_2\oplus\Sigma^{14,7}\mathbb{M}_2\oplus\Sigma^{14,8}\mathbb{M}_2\oplus\Sigma^{15,8}\mathbb{M}_2\oplus\Sigma^{16,8}\mathbb{M}_2\oplus\Sigma^{16,9}\mathbb{M}_2\oplus\Sigma^{17,9}\mathbb{M}_2\oplus\Sigma^{18,9}\mathbb{M}_2\oplus\Sigma^{18,10}\mathbb{M}_2\oplus\Sigma^{19,10}\mathbb{M}_2\oplus\Sigma^{20,10}\mathbb{M}_2\oplus\Sigma^{21,11}\mathbb{M}_2\oplus\Sigma^{22,11}\mathbb{M}_2.$$




The cohomology of $\text{Gr}_2(\mathbb{R}^{p,1})$

Theorem 19 of this paper gives a formula for $\text{Gr}_k(\mathbb{R}^{p,1})$ in terms of the partition function $\text{part}(n,k,m,t)$ which counts partitions of $n$ into $k$ non-negative numbers not exceeding $m$ where the Young diagram corresponding to the partition has trace $t$. Using this formula, $$H^{\ast,\ast}(\text{Gr}_2(\mathbb{R}^{p,1})) =\bigoplus_{i=0}^{2p-4}\bigoplus_{j=0}^2(\Sigma^{i,j}\mathbb{M}_2)^{\oplus \text{part}(i,2,p-2,j)}$$ or $$H^{\ast,\ast}(\text{Gr}_2(\mathbb{R}^{p,1})) =\mathbb{M}_2 \oplus \Sigma^{1,1}\mathbb{M}_2 \oplus \left(\bigoplus_{i=2}^{p-2}\Sigma^{i,1}\mathbb{M}_2\right)^{\oplus 2}\oplus \Sigma^{p-1,1}\mathbb{M}_2 \oplus \left(\Sigma^{p,2}\mathbb{M}_2\right)^{\oplus (\left\lfloor\frac i2\right\rfloor-1)}\oplus\bigoplus_{i=4}^{p-1}\left(\Sigma^{i,2}\mathbb{M}_2\oplus \Sigma^{2p-i,2}\mathbb{M}_2\right)^{\oplus (\left\lfloor\frac i2\right\rfloor-1)}. $$




The cohomology of $\text{Gr}_2(\mathbb{R}^{p,2})$

See Section 6 of this paper.
























The cohomology of $\text{Gr}_2(\mathbb{R}^{p,\left\lfloor \frac p2\right\rfloor})$

Yeah, what's the deal with these ones?