| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | (0,0,0) | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · |
| 1 | · | (8,2,0) | (12,2,1) | (15,4,1) | (18,5,2) | (21,5,4) | (23,8,4) | (25,10,5) | (27,11,7) | (29,11,10) | (30,15,10) | (31,18,11) | (32,20,13) | (33,21,16) | (34,21,20) | (34,25,21) | · | · | · |
| 2 | · | · | · | · | · | · | · | · | · | · | · | · | · | (30,30,15) | (32,30,18) | (33,31,21) | (34,31,25) | (34,33,28) | (34,34,32) |
Below is a plot displaying the Schur decomposition. In the \(\lambda=(\lambda_0,\lambda_1)\) spot we place \(\beta_{2,\lambda}(2,0;5)\), the multiplicity of \(\textbf{S}_{\lambda}\) occuring in the decomposition of \(K_{2,1}(2,0;5)\). Here \(\lambda\) is the weight \((\lambda_0,\lambda_1,\lambda_2)\) where \(\lambda_2\) is determined by the fact that \(|\lambda|\) equals \(d(p+q)+b\). The dominant weights are displayed in green. Click on an entry for more info!
Below is a plot displaying the multigraded Betti numbers. In the \((a_0,a_1)\) spot we place \(\beta_{2,\textbf{a}}(2,0;5)\). Here \(\textbf{a}\) is the weight \((a_0,a_1,a_2)\) where \(a_2\) is determined by the fact that \(|\textbf{a}|\) equals \(d(p+q)+b\). Entries with error corrected via our Schur decomposition algorithm are in orange. Click on an entry for more info!
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | · | · | · | · | 1 | 2 | 3 | 4 | 4 | 3 | 2 | 1 | · | · |
| 1 | · | · | 1 | 3 | 6 | 10 | 13 | 14 | 13 | 10 | 6 | 3 | 1 | · |
| 2 | · | 1 | 4 | 9 | 16 | 23 | 27 | 27 | 23 | 16 | 9 | 4 | 1 | · |
| 3 | · | 3 | 9 | 18 | 29 | 38 | 41 | 38 | 29 | 18 | 9 | 3 | · | · |
| 4 | 1 | 6 | 16 | 29 | 42 | 51 | 51 | 42 | 29 | 16 | 6 | 1 | · | · |
| 5 | 2 | 10 | 23 | 38 | 51 | 57 | 51 | 38 | 23 | 10 | 2 | · | · | · |
| 6 | 3 | 13 | 27 | 41 | 51 | 51 | 41 | 27 | 13 | 3 | · | · | · | · |
| 7 | 4 | 14 | 27 | 38 | 42 | 38 | 27 | 14 | 4 | · | · | · | · | · |
| 8 | 4 | 13 | 23 | 29 | 29 | 23 | 13 | 4 | · | · | · | · | · | · |
| 9 | 3 | 10 | 16 | 18 | 16 | 10 | 3 | · | · | · | · | · | · | · |
| 10 | 2 | 6 | 9 | 9 | 6 | 2 | · | · | · | · | · | · | · | · |
| 11 | 1 | 3 | 4 | 3 | 1 | · | · | · | · | · | · | · | · | · |
| 12 | · | 1 | 1 | · | · | · | · | · | · | · | · | · | · | · |
| 13 | · | · | · | · | · | · | · | · | · | · | · | · | · | · |