| 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 \(\beta_{7,\lambda}(2,2;4)\), the multiplicity of \(\textbf{S}_{\lambda}\) occuring in the decomposition of \(K_{7,1}(2,2;4)\). 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 \(\beta_{7,\textbf{a}}(2,2;4)\). 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!
| 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 4 | · | · | · | · | · | · | · | · | · | · | · | 1 | · | · | · |
| 5 | · | · | · | · | · | · | · | · | 1 | 2 | 4 | 4 | 2 | 1 | · |
| 6 | · | · | · | · | · | · | · | 2 | 6 | 12 | 13 | 12 | 6 | 2 | · |
| 7 | · | · | · | · | · | · | 3 | 11 | 25 | 33 | 33 | 25 | 11 | 3 | · |
| 8 | · | · | · | · | · | 4 | 15 | 38 | 58 | 68 | 58 | 38 | 15 | 4 | · |
| 9 | · | · | · | · | 4 | 17 | 46 | 80 | 106 | 106 | 80 | 46 | 17 | 4 | · |
| 10 | · | · | · | 3 | 15 | 46 | 87 | 130 | 147 | 130 | 87 | 46 | 15 | 3 | · |
| 11 | · | · | 2 | 11 | 38 | 80 | 130 | 165 | 165 | 130 | 80 | 38 | 11 | 2 | · |
| 12 | · | 1 | 6 | 25 | 58 | 106 | 147 | 165 | 147 | 106 | 58 | 25 | 6 | 1 | · |
| 13 | · | 2 | 12 | 33 | 68 | 106 | 130 | 130 | 106 | 68 | 33 | 12 | 2 | · | · |
| 14 | · | 4 | 13 | 33 | 58 | 80 | 87 | 80 | 58 | 33 | 13 | 4 | · | · | · |
| 15 | 1 | 4 | 12 | 25 | 38 | 46 | 46 | 38 | 25 | 12 | 4 | 1 | · | · | · |
| 16 | · | 2 | 6 | 11 | 15 | 17 | 15 | 11 | 6 | 2 | · | · | · | · | · |
| 17 | · | 1 | 2 | 3 | 4 | 4 | 3 | 2 | 1 | · | · | · | · | · | · |
| 18 | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · |