Current Betti Table Entry:
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| 0 |
(5,0,0) |
(11,1,0) |
(17,1,1) |
(22,3,1) |
(27,4,2) |
(32,4,4) |
(36,7,4) |
? |
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? |
(75,47,30) |
(77,47,35) |
(78,52,36) |
(79,56,38) |
(80,59,41) |
(81,61,45) |
(82,62,50) |
(83,62,56) |
(83,68,57) |
(83,73,59) |
(83,77,62) |
(83,80,66) |
(83,82,71) |
(83,83,77) |
| 2 |
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33 |
| 0 |
1 |
5 |
32 |
59 |
89 |
118 |
149 |
? |
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| 1 |
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344 |
327 |
305 |
280 |
254 |
224 |
193 |
158 |
128 |
95 |
66 |
36 |
6 |
1 |
| 2 |
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\(\lambda=(74,74,74)\)
- Multiplicity: 1
- Dimension: 1
- Dominant: No
\(\lambda=(77,76,69)\)
- Multiplicity: 8
- Dimension: 80
- Dominant: No
\(\lambda=(82,74,66)\)
- Multiplicity: 9
- Dimension: 729
- Dominant: No
\(\lambda=(80,78,64)\)
- Multiplicity: 6
- Dimension: 405
- Dominant: No
\(\lambda=(79,72,71)\)
- Multiplicity: 6
- Dimension: 80
- Dominant: No
\(\lambda=(77,75,70)\)
- Multiplicity: 9
- Dimension: 81
- Dominant: No
\(\lambda=(82,73,67)\)
- Multiplicity: 9
- Dimension: 595
- Dominant: No
\(\lambda=(80,77,65)\)
- Multiplicity: 9
- Dimension: 442
- Dominant: No
\(\lambda=(77,74,71)\)
- Multiplicity: 9
- Dimension: 64
- Dominant: No
\(\lambda=(82,72,68)\)
- Multiplicity: 7
- Dimension: 440
- Dominant: No
\(\lambda=(80,76,66)\)
- Multiplicity: 12
- Dimension: 440
- Dominant: No
\(\lambda=(77,73,72)\)
- Multiplicity: 4
- Dimension: 35
- Dominant: No
\(\lambda=(82,71,69)\)
- Multiplicity: 5
- Dimension: 270
- Dominant: No
\(\lambda=(83,77,62)\)
- Multiplicity: 1
- Dimension: 1288
- Dominant: Yes
\(\lambda=(80,75,67)\)
- Multiplicity: 14
- Dimension: 405
- Dominant: No
\(\lambda=(81,80,61)\)
- Multiplicity: 1
- Dimension: 440
- Dominant: No
\(\lambda=(82,70,70)\)
- Multiplicity: 2
- Dimension: 91
- Dominant: No
\(\lambda=(83,76,63)\)
- Multiplicity: 1
- Dimension: 1232
- Dominant: No
\(\lambda=(80,74,68)\)
- Multiplicity: 15
- Dimension: 343
- Dominant: No
\(\lambda=(78,78,66)\)
- Multiplicity: 4
- Dimension: 91
- Dominant: No
\(\lambda=(75,75,72)\)
- Multiplicity: 1
- Dimension: 10
- Dominant: No
\(\lambda=(78,77,67)\)
- Multiplicity: 7
- Dimension: 143
- Dominant: No
\(\lambda=(81,79,62)\)
- Multiplicity: 2
- Dimension: 567
- Dominant: No
\(\lambda=(83,75,64)\)
- Multiplicity: 2
- Dimension: 1134
- Dominant: No
\(\lambda=(80,73,69)\)
- Multiplicity: 12
- Dimension: 260
- Dominant: No
\(\lambda=(75,74,73)\)
- Multiplicity: 1
- Dimension: 8
- Dominant: No
\(\lambda=(78,76,68)\)
- Multiplicity: 12
- Dimension: 162
- Dominant: No
\(\lambda=(81,78,63)\)
- Multiplicity: 4
- Dimension: 640
- Dominant: No
\(\lambda=(83,74,65)\)
- Multiplicity: 3
- Dimension: 1000
- Dominant: No
\(\lambda=(80,72,70)\)
- Multiplicity: 9
- Dimension: 162
- Dominant: No
\(\lambda=(78,75,69)\)
- Multiplicity: 13
- Dimension: 154
- Dominant: No
\(\lambda=(81,77,64)\)
- Multiplicity: 6
- Dimension: 665
- Dominant: No
\(\lambda=(83,73,66)\)
- Multiplicity: 3
- Dimension: 836
- Dominant: No
\(\lambda=(80,71,71)\)
- Multiplicity: 3
- Dimension: 55
- Dominant: No
\(\lambda=(78,74,70)\)
- Multiplicity: 13
- Dimension: 125
- Dominant: No
\(\lambda=(81,76,65)\)
- Multiplicity: 9
- Dimension: 648
- Dominant: No
\(\lambda=(83,72,67)\)
- Multiplicity: 3
- Dimension: 648
- Dominant: No
\(\lambda=(78,73,71)\)
- Multiplicity: 8
- Dimension: 81
- Dominant: No
\(\lambda=(83,71,68)\)
- Multiplicity: 3
- Dimension: 442
- Dominant: No
\(\lambda=(81,75,66)\)
- Multiplicity: 11
- Dimension: 595
- Dominant: No
\(\lambda=(79,79,64)\)
- Multiplicity: 1
- Dimension: 136
- Dominant: No
\(\lambda=(76,76,70)\)
- Multiplicity: 6
- Dimension: 28
- Dominant: No
\(\lambda=(78,72,72)\)
- Multiplicity: 4
- Dimension: 28
- Dominant: No
\(\lambda=(83,70,69)\)
- Multiplicity: 1
- Dimension: 224
- Dominant: No
\(\lambda=(82,80,60)\)
- Multiplicity: 1
- Dimension: 756
- Dominant: Yes
\(\lambda=(81,74,67)\)
- Multiplicity: 12
- Dimension: 512
- Dominant: No
\(\lambda=(79,78,65)\)
- Multiplicity: 4
- Dimension: 224
- Dominant: No
\(\lambda=(76,75,71)\)
- Multiplicity: 5
- Dimension: 35
- Dominant: No
\(\lambda=(82,79,61)\)
- Multiplicity: 2
- Dimension: 874
- Dominant: No
\(\lambda=(81,73,68)\)
- Multiplicity: 11
- Dimension: 405
- Dominant: No
\(\lambda=(79,77,66)\)
- Multiplicity: 7
- Dimension: 270
- Dominant: No
\(\lambda=(76,74,72)\)
- Multiplicity: 6
- Dimension: 27
- Dominant: No
\(\lambda=(82,78,62)\)
- Multiplicity: 3
- Dimension: 935
- Dominant: No
\(\lambda=(81,72,69)\)
- Multiplicity: 9
- Dimension: 280
- Dominant: No
\(\lambda=(79,76,67)\)
- Multiplicity: 12
- Dimension: 280
- Dominant: No
\(\lambda=(76,73,73)\)
- Multiplicity: 1
- Dimension: 10
- Dominant: No
\(\lambda=(82,77,63)\)
- Multiplicity: 5
- Dimension: 945
- Dominant: No
\(\lambda=(81,71,70)\)
- Multiplicity: 5
- Dimension: 143
- Dominant: No
\(\lambda=(79,75,68)\)
- Multiplicity: 13
- Dimension: 260
- Dominant: No
\(\lambda=(82,76,64)\)
- Multiplicity: 7
- Dimension: 910
- Dominant: No
\(\lambda=(80,80,62)\)
- Multiplicity: 2
- Dimension: 190
- Dominant: No
\(\lambda=(79,74,69)\)
- Multiplicity: 14
- Dimension: 216
- Dominant: No
\(\lambda=(77,77,68)\)
- Multiplicity: 3
- Dimension: 55
- Dominant: No
\(\lambda=(82,75,65)\)
- Multiplicity: 8
- Dimension: 836
- Dominant: No
\(\lambda=(80,79,63)\)
- Multiplicity: 3
- Dimension: 323
- Dominant: No
\(\lambda=(79,73,70)\)
- Multiplicity: 11
- Dimension: 154
- Dominant: No
\(\textbf{a}=(78,66,78)\)
- Multiplicity: 263
- Dimension: 1
- Error: 0
\(\textbf{a}=(69,76,77)\)
- Multiplicity: 865
- Dimension: 1
- Error: 0
\(\textbf{a}=(80,78,64)\)
- Multiplicity: 73
- Dimension: 1
- Error: 0
\(\textbf{a}=(70,82,70)\)
- Multiplicity: 92
- Dimension: 1
- Error: 0
\(\textbf{a}=(79,72,71)\)
- Multiplicity: 736
- Dimension: 1
- Error: 0
\(\textbf{a}=(66,73,83)\)
- Multiplicity: 10
- Dimension: 1
- Error: 0
\(\textbf{a}=(76,69,77)\)
- Multiplicity: 865
- Dimension: 1
- Error: 0
\(\textbf{a}=(67,79,76)\)
- Multiplicity: 357
- Dimension: 1
- Error: 0
\(\textbf{a}=(78,81,63)\)
- Multiplicity: 27
- Dimension: 1
- Error: 0
\(\textbf{a}=(77,75,70)\)
- Multiplicity: 1091
- Dimension: 1
- Error: 0
\(\textbf{a}=(73,66,83)\)
- Multiplicity: 10
- Dimension: 1
- Error: 0
\(\textbf{a}=(64,76,82)\)
- Multiplicity: 24
- Dimension: 1
- Error: 0
\(\textbf{a}=(83,62,77)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(74,72,76)\)
- Multiplicity: 1589
- Dimension: 1
- Error: 0
\(\textbf{a}=(65,82,75)\)
- Multiplicity: 37
- Dimension: 1
- Error: 0
\(\textbf{a}=(75,78,69)\)
- Multiplicity: 766
- Dimension: 1
- Error: 0
\(\textbf{a}=(71,69,82)\)
- Multiplicity: 89
- Dimension: 1
- Error: 0
\(\textbf{a}=(62,79,81)\)
- Multiplicity: 13
- Dimension: 1
- Error: 0
\(\textbf{a}=(81,65,76)\)
- Multiplicity: 79
- Dimension: 1
- Error: 0
\(\textbf{a}=(82,71,69)\)
- Multiplicity: 89
- Dimension: 1
- Error: 0
\(\textbf{a}=(73,81,68)\)
- Multiplicity: 190
- Dimension: 1
- Error: 0
\(\textbf{a}=(83,77,62)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(72,75,75)\)
- Multiplicity: 1665
- Dimension: 1
- Error: 0
\(\textbf{a}=(78,62,82)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(69,72,81)\)
- Multiplicity: 218
- Dimension: 1
- Error: 0
\(\textbf{a}=(60,82,80)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(80,74,68)\)
- Multiplicity: 338
- Dimension: 1
- Error: 0
\(\textbf{a}=(81,80,61)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(70,78,74)\)
- Multiplicity: 922
- Dimension: 1
- Error: 0
\(\textbf{a}=(79,68,75)\)
- Multiplicity: 480
- Dimension: 1
- Error: 0
\(\textbf{a}=(76,65,81)\)
- Multiplicity: 79
- Dimension: 1
- Error: 0
\(\textbf{a}=(67,75,80)\)
- Multiplicity: 263
- Dimension: 1
- Error: 0
\(\textbf{a}=(78,77,67)\)
- Multiplicity: 413
- Dimension: 1
- Error: 0
\(\textbf{a}=(68,81,73)\)
- Multiplicity: 190
- Dimension: 1
- Error: 0
\(\textbf{a}=(77,71,74)\)
- Multiplicity: 1270
- Dimension: 1
- Error: 0
\(\textbf{a}=(74,68,80)\)
- Multiplicity: 338
- Dimension: 1
- Error: 0
\(\textbf{a}=(65,78,79)\)
- Multiplicity: 149
- Dimension: 1
- Error: 0
\(\textbf{a}=(76,80,66)\)
- Multiplicity: 189
- Dimension: 1
- Error: 0
\(\textbf{a}=(75,74,73)\)
- Multiplicity: 1806
- Dimension: 1
- Error: 0
\(\textbf{a}=(81,61,80)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(72,71,79)\)
- Multiplicity: 736
- Dimension: 1
- Error: 0
\(\textbf{a}=(63,81,78)\)
- Multiplicity: 27
- Dimension: 1
- Error: 0
\(\textbf{a}=(74,83,65)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(83,73,66)\)
- Multiplicity: 10
- Dimension: 1
- Error: 0
\(\textbf{a}=(73,77,72)\)
- Multiplicity: 1366
- Dimension: 1
- Error: 0
\(\textbf{a}=(82,67,73)\)
- Multiplicity: 67
- Dimension: 1
- Error: 0
\(\textbf{a}=(79,64,79)\)
- Multiplicity: 81
- Dimension: 1
- Error: 0
\(\textbf{a}=(70,74,78)\)
- Multiplicity: 922
- Dimension: 1
- Error: 0
\(\textbf{a}=(81,76,65)\)
- Multiplicity: 79
- Dimension: 1
- Error: 0
\(\textbf{a}=(71,80,71)\)
- Multiplicity: 461
- Dimension: 1
- Error: 0
\(\textbf{a}=(80,70,72)\)
- Multiplicity: 445
- Dimension: 1
- Error: 0
\(\textbf{a}=(77,67,78)\)
- Multiplicity: 413
- Dimension: 1
- Error: 0
\(\textbf{a}=(68,77,77)\)
- Multiplicity: 627
- Dimension: 1
- Error: 0
\(\textbf{a}=(79,79,64)\)
- Multiplicity: 81
- Dimension: 1
- Error: 0
\(\textbf{a}=(69,83,70)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(78,73,71)\)
- Multiplicity: 1026
- Dimension: 1
- Error: 0
\(\textbf{a}=(65,74,83)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(75,70,77)\)
- Multiplicity: 1091
- Dimension: 1
- Error: 0
\(\textbf{a}=(66,80,76)\)
- Multiplicity: 189
- Dimension: 1
- Error: 0
\(\textbf{a}=(77,82,63)\)
- Multiplicity: 14
- Dimension: 1
- Error: 0
\(\textbf{a}=(76,76,70)\)
- Multiplicity: 1158
- Dimension: 1
- Error: 0
\(\textbf{a}=(72,67,83)\)
- Multiplicity: 13
- Dimension: 1
- Error: 0
\(\textbf{a}=(63,77,82)\)
- Multiplicity: 14
- Dimension: 1
- Error: 0
\(\textbf{a}=(82,63,77)\)
- Multiplicity: 14
- Dimension: 1
- Error: 0
\(\textbf{a}=(73,73,76)\)
- Multiplicity: 1648
- Dimension: 1
- Error: 0
\(\textbf{a}=(64,83,75)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(83,69,70)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(74,79,69)\)
- Multiplicity: 596
- Dimension: 1
- Error: 0
\(\textbf{a}=(70,70,82)\)
- Multiplicity: 92
- Dimension: 1
- Error: 0
\(\textbf{a}=(61,80,81)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(80,66,76)\)
- Multiplicity: 189
- Dimension: 1
- Error: 0
\(\textbf{a}=(81,72,69)\)
- Multiplicity: 218
- Dimension: 1
- Error: 0
\(\textbf{a}=(72,82,68)\)
- Multiplicity: 80
- Dimension: 1
- Error: 0
\(\textbf{a}=(82,78,62)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(71,76,75)\)
- Multiplicity: 1412
- Dimension: 1
- Error: 0
\(\textbf{a}=(77,63,82)\)
- Multiplicity: 14
- Dimension: 1
- Error: 0
\(\textbf{a}=(68,73,81)\)
- Multiplicity: 190
- Dimension: 1
- Error: 0
\(\textbf{a}=(79,75,68)\)
- Multiplicity: 480
- Dimension: 1
- Error: 0
\(\textbf{a}=(80,81,61)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(69,79,74)\)
- Multiplicity: 596
- Dimension: 1
- Error: 0
\(\textbf{a}=(78,69,75)\)
- Multiplicity: 766
- Dimension: 1
- Error: 0
\(\textbf{a}=(75,66,81)\)
- Multiplicity: 115
- Dimension: 1
- Error: 0
\(\textbf{a}=(66,76,80)\)
- Multiplicity: 189
- Dimension: 1
- Error: 0
\(\textbf{a}=(77,78,67)\)
- Multiplicity: 413
- Dimension: 1
- Error: 0
\(\textbf{a}=(67,82,73)\)
- Multiplicity: 67
- Dimension: 1
- Error: 0
\(\textbf{a}=(76,72,74)\)
- Multiplicity: 1589
- Dimension: 1
- Error: 0
\(\textbf{a}=(73,69,80)\)
- Multiplicity: 401
- Dimension: 1
- Error: 0
\(\textbf{a}=(64,79,79)\)
- Multiplicity: 81
- Dimension: 1
- Error: 0
\(\textbf{a}=(75,81,66)\)
- Multiplicity: 115
- Dimension: 1
- Error: 0
\(\textbf{a}=(74,75,73)\)
- Multiplicity: 1806
- Dimension: 1
- Error: 0
\(\textbf{a}=(83,65,74)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(80,62,80)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(71,72,79)\)
- Multiplicity: 736
- Dimension: 1
- Error: 0
\(\textbf{a}=(62,82,78)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(82,74,66)\)
- Multiplicity: 52
- Dimension: 1
- Error: 0
\(\textbf{a}=(72,78,72)\)
- Multiplicity: 1064
- Dimension: 1
- Error: 0
\(\textbf{a}=(81,68,73)\)
- Multiplicity: 190
- Dimension: 1
- Error: 0
\(\textbf{a}=(78,65,79)\)
- Multiplicity: 149
- Dimension: 1
- Error: 0
\(\textbf{a}=(69,75,78)\)
- Multiplicity: 766
- Dimension: 1
- Error: 0
\(\textbf{a}=(80,77,65)\)
- Multiplicity: 124
- Dimension: 1
- Error: 0
\(\textbf{a}=(70,81,71)\)
- Multiplicity: 234
- Dimension: 1
- Error: 0
\(\textbf{a}=(79,71,72)\)
- Multiplicity: 736
- Dimension: 1
- Error: 0
\(\textbf{a}=(76,68,78)\)
- Multiplicity: 589
- Dimension: 1
- Error: 0
\(\textbf{a}=(67,78,77)\)
- Multiplicity: 413
- Dimension: 1
- Error: 0
\(\textbf{a}=(78,80,64)\)
- Multiplicity: 73
- Dimension: 1
- Error: 0
\(\textbf{a}=(77,74,71)\)
- Multiplicity: 1270
- Dimension: 1
- Error: 0
\(\textbf{a}=(64,75,83)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(74,71,77)\)
- Multiplicity: 1270
- Dimension: 1
- Error: 0
\(\textbf{a}=(65,81,76)\)
- Multiplicity: 79
- Dimension: 1
- Error: 0
\(\textbf{a}=(76,83,63)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(75,77,70)\)
- Multiplicity: 1091
- Dimension: 1
- Error: 0
\(\textbf{a}=(71,68,83)\)
- Multiplicity: 16
- Dimension: 1
- Error: 0
\(\textbf{a}=(62,78,82)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(81,64,77)\)
- Multiplicity: 49
- Dimension: 1
- Error: 0
\(\textbf{a}=(72,74,76)\)
- Multiplicity: 1589
- Dimension: 1
- Error: 0
\(\textbf{a}=(82,70,70)\)
- Multiplicity: 92
- Dimension: 1
- Error: 0
\(\textbf{a}=(73,80,69)\)
- Multiplicity: 401
- Dimension: 1
- Error: 0
\(\textbf{a}=(83,76,63)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(69,71,82)\)
- Multiplicity: 89
- Dimension: 1
- Error: 0
\(\textbf{a}=(60,81,81)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(79,67,76)\)
- Multiplicity: 357
- Dimension: 1
- Error: 0
\(\textbf{a}=(80,73,69)\)
- Multiplicity: 401
- Dimension: 1
- Error: 0
\(\textbf{a}=(71,83,68)\)
- Multiplicity: 16
- Dimension: 1
- Error: 0
\(\textbf{a}=(81,79,62)\)
- Multiplicity: 13
- Dimension: 1
- Error: 0
\(\textbf{a}=(70,77,75)\)
- Multiplicity: 1091
- Dimension: 1
- Error: 0
\(\textbf{a}=(76,64,82)\)
- Multiplicity: 24
- Dimension: 1
- Error: 0
\(\textbf{a}=(67,74,81)\)
- Multiplicity: 154
- Dimension: 1
- Error: 0
\(\textbf{a}=(78,76,68)\)
- Multiplicity: 589
- Dimension: 1
- Error: 0
\(\textbf{a}=(79,82,61)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(68,80,74)\)
- Multiplicity: 338
- Dimension: 1
- Error: 0
\(\textbf{a}=(77,70,75)\)
- Multiplicity: 1091
- Dimension: 1
- Error: 0
\(\textbf{a}=(74,67,81)\)
- Multiplicity: 154
- Dimension: 1
- Error: 0
\(\textbf{a}=(65,77,80)\)
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- Dimension: 1
- Error: 0
Below is a plot displaying the Schur decomposition. In the \(\lambda=(\lambda_0,\lambda_1)\) spot we place \(\beta_{30,\lambda}(2,5;7)\), the multiplicity of \(\textbf{S}_{\lambda}\) occuring in the decomposition of \(K_{30,1}(2,5;7)\). 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!
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Below is a plot displaying the multigraded Betti numbers. In the \((a_0,a_1)\) spot we place \(\beta_{30,\textbf{a}}(2,5;7)\). 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!