| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | (3,0,0) | (6,1,0) | (9,1,1) | (11,3,1) | (13,4,2) | (15,4,4) | (16,7,4) | (17,9,5) | (18,10,7) | (19,10,10) | · | · | · |
| 1 | · | · | · | · | · | · | · | (15,15,5) | (17,15,7) | (18,16,9) | (19,16,12) | (19,18,14) | (19,19,17) |
| 2 | · | · | · | · | · | · | · | · | · | · | · | · | · |
Below is a plot displaying the Schur decomposition. In the \(\lambda=(\lambda_0,\lambda_1)\) spot we place \(\beta_{3,\lambda}(2,3;4)\), the multiplicity of \(\textbf{S}_{\lambda}\) occuring in the decomposition of \(K_{3,0}(2,3;4)\). 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 \(\beta_{3,\textbf{a}}(2,3;4)\). 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 | · | · | · | 1 | 3 | 6 | 9 | 10 | 9 | 6 | 3 | 1 | · |
| 2 | · | · | 1 | 5 | 12 | 20 | 26 | 26 | 20 | 12 | 5 | 1 | · |
| 3 | · | 1 | 5 | 16 | 30 | 44 | 50 | 44 | 30 | 16 | 5 | 1 | · |
| 4 | · | 3 | 12 | 30 | 51 | 66 | 66 | 51 | 30 | 12 | 3 | · | · |
| 5 | · | 6 | 20 | 44 | 66 | 76 | 66 | 44 | 20 | 6 | · | · | · |
| 6 | 1 | 9 | 26 | 50 | 66 | 66 | 50 | 26 | 9 | 1 | · | · | · |
| 7 | 1 | 10 | 26 | 44 | 51 | 44 | 26 | 10 | 1 | · | · | · | · |
| 8 | 1 | 9 | 20 | 30 | 30 | 20 | 9 | 1 | · | · | · | · | · |
| 9 | 1 | 6 | 12 | 16 | 12 | 6 | 1 | · | · | · | · | · | · |
| 10 | · | 3 | 5 | 5 | 3 | · | · | · | · | · | · | · | · |
| 11 | · | 1 | 1 | 1 | · | · | · | · | · | · | · | · | · |
| 12 | · | · | · | · | · | · | · | · | · | · | · | · | · |