| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | (1,0,0) | (4,1,0) | (7,1,1) | · | · | · | · | · | · | · | · | · | · |
| 1 | · | · | (8,5,0) | (11,5,1) | (13,6,2) | (15,6,4) | (16,9,4) | (17,11,5) | (18,12,7) | (19,12,10) | (19,15,11) | (19,17,13) | · |
| 2 | · | · | · | · | · | · | · | · | · | · | · | · | (19,19,19) |
Below is a plot displaying the Schur decomposition. In the \(\lambda=(\lambda_0,\lambda_1)\) spot we place \(\beta_{3,\lambda}(2,1;4)\), the multiplicity of \(\textbf{S}_{\lambda}\) occuring in the decomposition of \(K_{3,1}(2,1;4)\). 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 \(\beta_{3,\textbf{a}}(2,1;4)\). 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 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | · | · | · | · | · | · | · | · | 1 | 1 | · | · | · |
| 1 | · | · | · | · | · | 1 | 2 | 4 | 5 | 4 | 2 | 1 | · |
| 2 | · | · | · | · | 1 | 4 | 8 | 11 | 11 | 8 | 4 | 1 | · |
| 3 | · | · | · | 2 | 5 | 13 | 19 | 22 | 19 | 13 | 5 | 2 | · |
| 4 | · | · | 1 | 5 | 13 | 24 | 30 | 30 | 24 | 13 | 5 | 1 | · |
| 5 | · | 1 | 4 | 13 | 24 | 36 | 39 | 36 | 24 | 13 | 4 | 1 | · |
| 6 | · | 2 | 8 | 19 | 30 | 39 | 39 | 30 | 19 | 8 | 2 | · | · |
| 7 | · | 4 | 11 | 22 | 30 | 36 | 30 | 22 | 11 | 4 | · | · | · |
| 8 | 1 | 5 | 11 | 19 | 24 | 24 | 19 | 11 | 5 | 1 | · | · | · |
| 9 | 1 | 4 | 8 | 13 | 13 | 13 | 8 | 4 | 1 | · | · | · | · |
| 10 | · | 2 | 4 | 5 | 5 | 4 | 2 | · | · | · | · | · | · |
| 11 | · | 1 | 1 | 2 | 1 | 1 | · | · | · | · | · | · | · |
| 12 | · | · | · | · | · | · | · | · | · | · | · | · | · |