| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | (2,0,0) | (6,1,0) | (10,1,1) | (13,3,1) | (16,4,2) | (19,4,4) | · | · | · | · | · | · | · | · | · | · | · | · | · |
| 1 | · | · | · | (13,9,0) | (17,9,1) | (20,10,2) | (23,10,4) | (25,12,5) | (27,13,7) | (29,13,10) | (30,17,10) | (31,20,11) | (32,22,13) | (33,23,16) | (34,23,20) | (34,27,21) | (34,30,23) | (34,32,26) | · |
| 2 | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | (34,34,34) |
Below is a plot displaying the Schur decomposition. In the \lambda=(\lambda_0,\lambda_1) spot we place \beta_{12,\lambda}(2,2;5), the multiplicity of \textbf{S}_{\lambda} occuring in the decomposition of K_{12,1}(2,2;5). 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!
| 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 17 | · | · | · | · | · | · | · | · | · | · | · | · |
| 18 | · | · | · | · | · | · | · | · | · | 2 | 1 | · |
| 19 | · | · | · | · | · | · | · | 10 | 10 | 6 | 2 | · |
| 20 | · | · | · | · | · | 15 | 25 | 23 | 16 | 7 | 2 | · |
| 21 | · | · | · | 14 | 31 | 43 | 42 | 32 | 18 | 7 | 1 | · |
| 22 | · | 4 | 17 | 35 | 51 | 55 | 47 | 31 | 16 | 5 | 1 | · |
| 23 | · | 8 | 24 | 43 | 54 | 54 | 41 | 25 | 11 | 3 | · | · |
| 24 | · | · | 16 | 33 | 42 | 39 | 28 | 15 | 6 | 1 | · | · |
| 25 | · | · | · | 16 | 25 | 24 | 16 | 8 | 3 | · | · | · |
| 26 | · | · | · | · | 9 | 11 | 7 | 3 | 1 | · | · | · |
| 27 | · | · | · | · | · | 3 | 2 | 1 | · | · | · | · |
| 28 | · | · | · | · | · | · | · | · | · | · | · | · |
Below is a plot displaying the multigraded Betti numbers. In the (a_0,a_1) spot we place \beta_{12,\textbf{a}}(2,2;5). 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!