| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | (3,0,0) | (7,1,0) | (11,1,1) | (14,3,1) | (17,4,2) | (20,4,4) | (22,7,4) | (24,9,5) | (26,10,7) | (28,10,10) | · | · | · | · | · | · | · | · | · |
| 1 | · | · | · | · | (14,14,0) | (18,14,1) | (21,15,2) | (24,15,4) | (26,17,5) | (28,18,7) | (30,18,10) | (31,21,11) | (32,23,13) | (33,24,16) | (34,24,20) | (34,28,21) | (34,31,23) | (34,33,26) | (34,34,30) |
| 2 | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · |
Below is a plot displaying the Schur decomposition. In the \(\lambda=(\lambda_0,\lambda_1)\) spot we place \(\beta_{3,\lambda}(2,3;5)\), the multiplicity of \(\textbf{S}_{\lambda}\) occuring in the decomposition of \(K_{3,0}(2,3;5)\). 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 \(\beta_{3,\textbf{a}}(2,3;5)\). 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 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | · | · | · | · | · | · | 1 | 1 | 2 | 2 | 2 | 1 | 1 | · | · | · |
| 1 | · | · | · | 1 | 3 | 6 | 10 | 14 | 16 | 16 | 14 | 10 | 6 | 3 | 1 | · |
| 2 | · | · | 1 | 5 | 12 | 21 | 33 | 41 | 44 | 41 | 33 | 21 | 12 | 5 | 1 | · |
| 3 | · | 1 | 5 | 16 | 31 | 52 | 72 | 83 | 83 | 72 | 52 | 31 | 16 | 5 | 1 | · |
| 4 | · | 3 | 12 | 31 | 59 | 90 | 115 | 125 | 115 | 90 | 59 | 31 | 12 | 3 | · | · |
| 5 | · | 6 | 21 | 52 | 90 | 128 | 153 | 153 | 128 | 90 | 52 | 21 | 6 | · | · | · |
| 6 | 1 | 10 | 33 | 72 | 115 | 153 | 168 | 153 | 115 | 72 | 33 | 10 | 1 | · | · | · |
| 7 | 1 | 14 | 41 | 83 | 125 | 153 | 153 | 125 | 83 | 41 | 14 | 1 | · | · | · | · |
| 8 | 2 | 16 | 44 | 83 | 115 | 128 | 115 | 83 | 44 | 16 | 2 | · | · | · | · | · |
| 9 | 2 | 16 | 41 | 72 | 90 | 90 | 72 | 41 | 16 | 2 | · | · | · | · | · | · |
| 10 | 2 | 14 | 33 | 52 | 59 | 52 | 33 | 14 | 2 | · | · | · | · | · | · | · |
| 11 | 1 | 10 | 21 | 31 | 31 | 21 | 10 | 1 | · | · | · | · | · | · | · | · |
| 12 | 1 | 6 | 12 | 16 | 12 | 6 | 1 | · | · | · | · | · | · | · | · | · |
| 13 | · | 3 | 5 | 5 | 3 | · | · | · | · | · | · | · | · | · | · | · |
| 14 | · | 1 | 1 | 1 | · | · | · | · | · | · | · | · | · | · | · | · |
| 15 | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · |