| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | (2,0,0) | (6,1,0) | (10,1,1) | (13,3,1) | (16,4,2) | (19,4,4) | · | · | · | · | · | · | · | · | · | · | · | · | · |
| 1 | · | · | · | (13,9,0) | (17,9,1) | (20,10,2) | (23,10,4) | (25,12,5) | (27,13,7) | (29,13,10) | (30,17,10) | (31,20,11) | (32,22,13) | (33,23,16) | (34,23,20) | (34,27,21) | (34,30,23) | (34,32,26) | · |
| 2 | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | (34,34,34) |
Below is a plot displaying the Schur decomposition. In the \(\lambda=(\lambda_0,\lambda_1)\) spot we place \(\beta_{3,\lambda}(2,2;5)\), the multiplicity of \(\textbf{S}_{\lambda}\) occuring in the decomposition of \(K_{3,0}(2,2;5)\). 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 \(\beta_{3,\textbf{a}}(2,2;5)\). 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!
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | · | · | 1 | 2 | 3 | 5 | 6 | 6 | 6 | 5 | 3 | 2 | 1 | · |
| 2 | · | 1 | 4 | 7 | 12 | 17 | 19 | 19 | 17 | 12 | 7 | 4 | 1 | · |
| 3 | 1 | 4 | 10 | 18 | 28 | 35 | 38 | 35 | 28 | 18 | 10 | 4 | 1 | · |
| 4 | 2 | 7 | 18 | 31 | 44 | 53 | 53 | 44 | 31 | 18 | 7 | 2 | · | · |
| 5 | 3 | 12 | 28 | 44 | 60 | 66 | 60 | 44 | 28 | 12 | 3 | · | · | · |
| 6 | 5 | 17 | 35 | 53 | 66 | 66 | 53 | 35 | 17 | 5 | · | · | · | · |
| 7 | 6 | 19 | 38 | 53 | 60 | 53 | 38 | 19 | 6 | · | · | · | · | · |
| 8 | 6 | 19 | 35 | 44 | 44 | 35 | 19 | 6 | · | · | · | · | · | · |
| 9 | 6 | 17 | 28 | 31 | 28 | 17 | 6 | · | · | · | · | · | · | · |
| 10 | 5 | 12 | 18 | 18 | 12 | 5 | · | · | · | · | · | · | · | · |
| 11 | 3 | 7 | 10 | 7 | 3 | · | · | · | · | · | · | · | · | · |
| 12 | 2 | 4 | 4 | 2 | · | · | · | · | · | · | · | · | · | · |
| 13 | 1 | 1 | 1 | · | · | · | · | · | · | · | · | · | · | · |
| 14 | · | · | · | · | · | · | · | · | · | · | · | · | · | · |