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