| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | (0,0,0) | · | · | · | · | · | · | · | · | · | · | · | · |
| 1 | · | (6,2,0) | (9,2,1) | (11,4,1) | (13,5,2) | (15,5,4) | (16,8,4) | (17,10,5) | (18,11,7) | (19,11,10) | (19,14,11) | · | · |
| 2 | · | · | · | · | · | · | · | · | · | · | (18,18,12) | (19,18,15) | (19,19,18) |
Below is a plot displaying the Schur decomposition. In the \(\lambda=(\lambda_0,\lambda_1)\) spot we place \(\beta_{3,\lambda}(2,0;4)\), the multiplicity of \(\textbf{S}_{\lambda}\) occuring in the decomposition of \(K_{3,1}(2,0;4)\). 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 \(\beta_{3,\textbf{a}}(2,0;4)\). 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 | · | · | · | · | 1 | 3 | 6 | 8 | 8 | 6 | 3 | 1 | · |
| 2 | · | · | · | 2 | 6 | 14 | 20 | 24 | 20 | 14 | 6 | 2 | · |
| 3 | · | · | 2 | 8 | 20 | 34 | 44 | 44 | 34 | 20 | 8 | 2 | · |
| 4 | · | 1 | 6 | 20 | 39 | 59 | 65 | 59 | 39 | 20 | 6 | 1 | · |
| 5 | · | 3 | 14 | 34 | 59 | 76 | 76 | 59 | 34 | 14 | 3 | · | · |
| 6 | · | 6 | 20 | 44 | 65 | 76 | 65 | 44 | 20 | 6 | · | · | · |
| 7 | 1 | 8 | 24 | 44 | 59 | 59 | 44 | 24 | 8 | 1 | · | · | · |
| 8 | 1 | 8 | 20 | 34 | 39 | 34 | 20 | 8 | 1 | · | · | · | · |
| 9 | 1 | 6 | 14 | 20 | 20 | 14 | 6 | 1 | · | · | · | · | · |
| 10 | · | 3 | 6 | 8 | 6 | 3 | · | · | · | · | · | · | · |
| 11 | · | 1 | 2 | 2 | 1 | · | · | · | · | · | · | · | · |
| 12 | · | · | · | · | · | · | · | · | · | · | · | · | · |