| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 10 | 225 | 2376 | 15525 | 69300 | 218295 | 473290 | 604934 | 143261 | 52852 | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · |
| 1 | · | · | · | · | 945 | 17890 | 172304 | 1167911 | 6181777 | 17305200 | 35102025 | 56163240 | 73547100 | 80233200 | 73547100 | 56831850 | 36989865 | 20189400 | 9164925 | 3415500 | 1024650 | 240120 | 41850 | 4950 | 315 | · |
| 2 | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | 1 |
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | (3,0,0) | (8,1,0) | (13,1,1) | (17,3,1) | (21,4,2) | (25,4,4) | (28,7,4) | (31,9,5) | (34,10,7) | (37,10,10) | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · |
| 1 | · | · | · | · | (19,14,0) | (24,14,1) | (28,15,2) | (32,15,4) | (35,17,5) | (38,18,7) | (41,18,10) | (43,21,11) | (45,23,13) | (47,24,16) | (49,24,20) | (50,29,20) | (51,33,21) | (52,36,23) | (53,38,26) | (54,39,30) | (55,39,35) | (55,44,36) | (55,48,38) | (55,51,41) | (55,53,45) | · |
| 2 | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | (55,55,55) |
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 3 | 20 | 88 | 294 | 759 | 1434 | 1705 | 242 | 139 | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · |
| 1 | · | · | · | · | 1 | 21 | 239 | 1482 | 10408 | 29087 | 57953 | 91464 | 119370 | 131367 | 123120 | 98722 | 67750 | 39685 | 19743 | 8263 | 2865 | 808 | 179 | 28 | 3 | · |
| 2 | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | · | 1 |
Below is a plot displaying the Schur decomposition. In the \(\lambda=(\lambda_0,\lambda_1)\) spot we place \(\beta_{1,\lambda}(2,3;6)\), the multiplicity of \(\textbf{S}_{\lambda}\) occuring in the decomposition of \(K_{1,0}(2,3;6)\). 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 \(\beta_{1,\textbf{a}}(2,3;6)\). 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!