| 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 \(\beta_{4,\lambda}(2,1;4)\), the multiplicity of \(\textbf{S}_{\lambda}\) occuring in the decomposition of \(K_{4,1}(2,1;4)\). 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 \(\beta_{4,\textbf{a}}(2,1;4)\). 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!
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | · | · | · | · | · | · | · | 1 | 2 | 2 | 2 | 1 | · | · |
| 2 | · | · | · | · | · | 1 | 3 | 7 | 10 | 10 | 7 | 3 | 1 | · |
| 3 | · | · | · | · | 2 | 7 | 15 | 24 | 28 | 24 | 15 | 7 | 2 | · |
| 4 | · | · | · | 2 | 9 | 23 | 39 | 52 | 52 | 39 | 23 | 9 | 2 | · |
| 5 | · | · | 2 | 9 | 26 | 51 | 74 | 84 | 74 | 51 | 26 | 9 | 2 | · |
| 6 | · | 1 | 7 | 23 | 51 | 84 | 105 | 105 | 84 | 51 | 23 | 7 | 1 | · |
| 7 | · | 3 | 15 | 39 | 74 | 105 | 116 | 105 | 74 | 39 | 15 | 3 | · | · |
| 8 | 1 | 7 | 24 | 52 | 84 | 105 | 105 | 84 | 52 | 24 | 7 | 1 | · | · |
| 9 | 2 | 10 | 28 | 52 | 74 | 84 | 74 | 52 | 28 | 10 | 2 | · | · | · |
| 10 | 2 | 10 | 24 | 39 | 51 | 51 | 39 | 24 | 10 | 2 | · | · | · | · |
| 11 | 2 | 7 | 15 | 23 | 26 | 23 | 15 | 7 | 2 | · | · | · | · | · |
| 12 | 1 | 3 | 7 | 9 | 9 | 7 | 3 | 1 | · | · | · | · | · | · |
| 13 | · | 1 | 2 | 2 | 2 | 1 | · | · | · | · | · | · | · | · |
| 14 | · | · | · | · | · | · | · | · | · | · | · | · | · | · |