| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | (1,0,0) | (5,1,0) | (9,1,1) | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · |
| 1 | · | · | (11,5,0) | (15,5,1) | (18,6,2) | (21,6,4) | (23,9,4) | (25,11,5) | (27,12,7) | (29,12,10) | (30,16,10) | (31,19,11) | (32,21,13) | (33,22,16) | (34,22,20) | (34,26,21) | (34,29,23) | · | · |
| 2 | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | (33,33,25) | (34,33,29) | (34,34,33) |
Below is a plot displaying the Schur decomposition. In the \(\lambda=(\lambda_0,\lambda_1)\) spot we place \(\beta_{3,\lambda}(2,1;5)\), the multiplicity of \(\textbf{S}_{\lambda}\) occuring in the decomposition of \(K_{3,1}(2,1;5)\). 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 \(\beta_{3,\textbf{a}}(2,1;5)\). 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 | 14 | 15 | 16 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | · | · | · | · | · | · | · | · | 1 | 2 | 2 | 2 | 2 | 1 | · | · | · |
| 1 | · | · | · | · | · | 1 | 2 | 5 | 8 | 11 | 11 | 11 | 8 | 5 | 2 | 1 | · |
| 2 | · | · | · | · | 1 | 4 | 9 | 16 | 23 | 27 | 27 | 23 | 16 | 9 | 4 | 1 | · |
| 3 | · | · | · | 2 | 5 | 14 | 25 | 39 | 48 | 54 | 48 | 39 | 25 | 14 | 5 | 2 | · |
| 4 | · | · | 1 | 5 | 14 | 30 | 49 | 67 | 79 | 79 | 67 | 49 | 30 | 14 | 5 | 1 | · |
| 5 | · | 1 | 4 | 14 | 30 | 56 | 80 | 103 | 109 | 103 | 80 | 56 | 30 | 14 | 4 | 1 | · |
| 6 | · | 2 | 9 | 25 | 49 | 80 | 109 | 126 | 126 | 109 | 80 | 49 | 25 | 9 | 2 | · | · |
| 7 | · | 5 | 16 | 39 | 67 | 103 | 126 | 138 | 126 | 103 | 67 | 39 | 16 | 5 | · | · | · |
| 8 | 1 | 8 | 23 | 48 | 79 | 109 | 126 | 126 | 109 | 79 | 48 | 23 | 8 | 1 | · | · | · |
| 9 | 2 | 11 | 27 | 54 | 79 | 103 | 109 | 103 | 79 | 54 | 27 | 11 | 2 | · | · | · | · |
| 10 | 2 | 11 | 27 | 48 | 67 | 80 | 80 | 67 | 48 | 27 | 11 | 2 | · | · | · | · | · |
| 11 | 2 | 11 | 23 | 39 | 49 | 56 | 49 | 39 | 23 | 11 | 2 | · | · | · | · | · | · |
| 12 | 2 | 8 | 16 | 25 | 30 | 30 | 25 | 16 | 8 | 2 | · | · | · | · | · | · | · |
| 13 | 1 | 5 | 9 | 14 | 14 | 14 | 9 | 5 | 1 | · | · | · | · | · | · | · | · |
| 14 | · | 2 | 4 | 5 | 5 | 4 | 2 | · | · | · | · | · | · | · | · | · | · |
| 15 | · | 1 | 1 | 2 | 1 | 1 | · | · | · | · | · | · | · | · | · | · | · |
| 16 | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · |