| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | (4,0,0) | (8,1,0) | (12,1,1) | (15,3,1) | (18,4,2) | (21,4,4) | (23,7,4) | (25,9,5) | (27,10,7) | (29,10,10) | (30,14,10) | (31,17,11) | (32,19,13) | (33,20,16) | (34,20,20) | · | · | · | · |
| 1 | · | · | · | · | · | · | · | · | · | (24,24,6) | (27,24,8) | (29,25,10) | (31,25,13) | (32,27,15) | (33,28,18) | (34,28,22) | (34,31,24) | (34,33,27) | (34,34,31) |
| 2 | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · |
Below is a plot displaying the Schur decomposition. In the \(\lambda=(\lambda_0,\lambda_1)\) spot we place \(\beta_{2,\lambda}(2,4;5)\), the multiplicity of \(\textbf{S}_{\lambda}\) occuring in the decomposition of \(K_{2,0}(2,4;5)\). 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 \(\beta_{2,\textbf{a}}(2,4;5)\). 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 | 4 | 5 | 6 | 5 | 4 | 2 | 1 | · | · |
| 1 | · | 1 | 3 | 7 | 12 | 17 | 20 | 20 | 17 | 12 | 7 | 3 | 1 | · |
| 2 | · | 3 | 8 | 17 | 26 | 35 | 37 | 35 | 26 | 17 | 8 | 3 | · | · |
| 3 | 1 | 7 | 17 | 31 | 45 | 54 | 54 | 45 | 31 | 17 | 7 | 1 | · | · |
| 4 | 2 | 12 | 26 | 45 | 59 | 67 | 59 | 45 | 26 | 12 | 2 | · | · | · |
| 5 | 4 | 17 | 35 | 54 | 67 | 67 | 54 | 35 | 17 | 4 | · | · | · | · |
| 6 | 5 | 20 | 37 | 54 | 59 | 54 | 37 | 20 | 5 | · | · | · | · | · |
| 7 | 6 | 20 | 35 | 45 | 45 | 35 | 20 | 6 | · | · | · | · | · | · |
| 8 | 5 | 17 | 26 | 31 | 26 | 17 | 5 | · | · | · | · | · | · | · |
| 9 | 4 | 12 | 17 | 17 | 12 | 4 | · | · | · | · | · | · | · | · |
| 10 | 2 | 7 | 8 | 7 | 2 | · | · | · | · | · | · | · | · | · |
| 11 | 1 | 3 | 3 | 1 | · | · | · | · | · | · | · | · | · | · |
| 12 | · | 1 | · | · | · | · | · | · | · | · | · | · | · | · |
| 13 | · | · | · | · | · | · | · | · | · | · | · | · | · | · |