Current Betti Table Entry:
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0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
0 |
(0,0,0) |
· |
· |
· |
· |
· |
· |
· |
· |
· |
· |
· |
· |
· |
· |
· |
· |
· |
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1 |
· |
(8,2,0) |
(12,2,1) |
(15,4,1) |
(18,5,2) |
(21,5,4) |
(23,8,4) |
(25,10,5) |
(27,11,7) |
(29,11,10) |
(30,15,10) |
(31,18,11) |
(32,20,13) |
(33,21,16) |
(34,21,20) |
(34,25,21) |
· |
· |
· |
2 |
· |
· |
· |
· |
· |
· |
· |
· |
· |
· |
· |
· |
· |
(30,30,15) |
(32,30,18) |
(33,31,21) |
(34,31,25) |
(34,33,28) |
(34,34,32) |
\(\lambda=(29,27,24)\)
- Multiplicity: 2
- Dimension: 42
- Dominant: No
\(\lambda=(30,29,21)\)
- Multiplicity: 1
- Dimension: 99
- Dominant: No
\(\lambda=(31,27,22)\)
- Multiplicity: 2
- Dimension: 165
- Dominant: No
\(\lambda=(28,28,24)\)
- Multiplicity: 2
- Dimension: 15
- Dominant: No
\(\lambda=(29,26,25)\)
- Multiplicity: 1
- Dimension: 24
- Dominant: No
\(\lambda=(30,28,22)\)
- Multiplicity: 3
- Dimension: 105
- Dominant: No
\(\lambda=(31,30,19)\)
- Multiplicity: 1
- Dimension: 168
- Dominant: No
\(\lambda=(32,24,24)\)
- Multiplicity: 2
- Dimension: 45
- Dominant: No
\(\lambda=(32,28,20)\)
- Multiplicity: 2
- Dimension: 315
- Dominant: No
\(\lambda=(31,26,23)\)
- Multiplicity: 2
- Dimension: 120
- Dominant: No
\(\lambda=(28,27,25)\)
- Multiplicity: 1
- Dimension: 15
- Dominant: No
\(\lambda=(30,27,23)\)
- Multiplicity: 2
- Dimension: 90
- Dominant: No
\(\lambda=(32,27,21)\)
- Multiplicity: 1
- Dimension: 273
- Dominant: No
\(\lambda=(31,29,20)\)
- Multiplicity: 1
- Dimension: 195
- Dominant: No
\(\lambda=(31,25,24)\)
- Multiplicity: 1
- Dimension: 63
- Dominant: No
\(\lambda=(28,26,26)\)
- Multiplicity: 1
- Dimension: 6
- Dominant: No
\(\lambda=(29,28,23)\)
- Multiplicity: 2
- Dimension: 48
- Dominant: No
\(\lambda=(30,26,24)\)
- Multiplicity: 3
- Dimension: 60
- Dominant: No
\(\lambda=(32,26,22)\)
- Multiplicity: 2
- Dimension: 210
- Dominant: No
\(\lambda=(32,30,18)\)
- Multiplicity: 1
- Dimension: 312
- Dominant: Yes
\(\lambda=(31,28,21)\)
- Multiplicity: 2
- Dimension: 192
- Dominant: No
\(\lambda=(30,30,20)\)
- Multiplicity: 1
- Dimension: 66
- Dominant: No
\(\textbf{a}=(28,21,31)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(19,31,30)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,27,24)\)
- Multiplicity: 65
- Dimension: 1
- Error: 0
\(\textbf{a}=(24,29,27)\)
- Multiplicity: 65
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,24,30)\)
- Multiplicity: 47
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,30,23)\)
- Multiplicity: 37
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,28,20)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(22,32,26)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,22,27)\)
- Multiplicity: 16
- Dimension: 1
- Error: 0
\(\textbf{a}=(19,29,32)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(24,27,29)\)
- Multiplicity: 65
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,31,19)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,25,26)\)
- Multiplicity: 74
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,22,32)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,28,25)\)
- Multiplicity: 93
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,26,22)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(22,30,28)\)
- Multiplicity: 28
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,20,29)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(24,25,31)\)
- Multiplicity: 23
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,31,24)\)
- Multiplicity: 23
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,29,21)\)
- Multiplicity: 16
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,23,28)\)
- Multiplicity: 48
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,18,31)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(22,28,30)\)
- Multiplicity: 28
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,24,24)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,32,20)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,26,27)\)
- Multiplicity: 110
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,21,30)\)
- Multiplicity: 16
- Dimension: 1
- Error: 0
\(\textbf{a}=(20,31,29)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,27,23)\)
- Multiplicity: 37
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,29,26)\)
- Multiplicity: 74
- Dimension: 1
- Error: 0
\(\textbf{a}=(22,26,32)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,30,22)\)
- Multiplicity: 28
- Dimension: 1
- Error: 0
\(\textbf{a}=(23,32,25)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,22,26)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,24,29)\)
- Multiplicity: 65
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,19,32)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(20,29,31)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,25,25)\)
- Multiplicity: 48
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,31,18)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,27,28)\)
- Multiplicity: 93
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,22,31)\)
- Multiplicity: 16
- Dimension: 1
- Error: 0
\(\textbf{a}=(18,32,30)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,28,24)\)
- Multiplicity: 76
- Dimension: 1
- Error: 0
\(\textbf{a}=(23,30,27)\)
- Multiplicity: 37
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,20,28)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,25,30)\)
- Multiplicity: 48
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,31,23)\)
- Multiplicity: 20
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,29,20)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,23,27)\)
- Multiplicity: 37
- Dimension: 1
- Error: 0
\(\textbf{a}=(18,30,32)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,18,30)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(23,28,29)\)
- Multiplicity: 48
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,32,19)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,26,26)\)
- Multiplicity: 102
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,23,32)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,27,22)\)
- Multiplicity: 16
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,29,25)\)
- Multiplicity: 74
- Dimension: 1
- Error: 0
\(\textbf{a}=(21,31,28)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,21,29)\)
- Multiplicity: 16
- Dimension: 1
- Error: 0
\(\textbf{a}=(23,26,31)\)
- Multiplicity: 20
- Dimension: 1
- Error: 0
\(\textbf{a}=(24,32,24)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,30,21)\)
- Multiplicity: 16
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,24,28)\)
- Multiplicity: 76
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,19,31)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(21,29,30)\)
- Multiplicity: 16
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,25,24)\)
- Multiplicity: 23
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,27,27)\)
- Multiplicity: 110
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,22,30)\)
- Multiplicity: 28
- Dimension: 1
- Error: 0
\(\textbf{a}=(19,32,29)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,28,23)\)
- Multiplicity: 48
- Dimension: 1
- Error: 0
\(\textbf{a}=(24,30,26)\)
- Multiplicity: 47
- Dimension: 1
- Error: 0
\(\textbf{a}=(21,27,32)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,29,19)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,31,22)\)
- Multiplicity: 16
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,23,26)\)
- Multiplicity: 20
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,25,29)\)
- Multiplicity: 74
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,20,32)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(19,30,31)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,26,25)\)
- Multiplicity: 74
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,32,18)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(24,28,28)\)
- Multiplicity: 76
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,23,31)\)
- Multiplicity: 20
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,29,24)\)
- Multiplicity: 65
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,27,21)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(22,31,27)\)
- Multiplicity: 16
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,21,28)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(24,26,30)\)
- Multiplicity: 47
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,32,23)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,30,20)\)
- Multiplicity: 9
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,24,27)\)
- Multiplicity: 65
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,19,30)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(22,29,29)\)
- Multiplicity: 30
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,25,23)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,27,26)\)
- Multiplicity: 110
- Dimension: 1
- Error: 0
\(\textbf{a}=(24,24,32)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,28,22)\)
- Multiplicity: 28
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,30,25)\)
- Multiplicity: 48
- Dimension: 1
- Error: 0
\(\textbf{a}=(20,32,28)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,22,29)\)
- Multiplicity: 30
- Dimension: 1
- Error: 0
\(\textbf{a}=(22,27,31)\)
- Multiplicity: 16
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,23,25)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,31,21)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,25,28)\)
- Multiplicity: 93
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,20,31)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(20,30,30)\)
- Multiplicity: 9
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,26,24)\)
- Multiplicity: 47
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,28,27)\)
- Multiplicity: 93
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,23,30)\)
- Multiplicity: 37
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,29,23)\)
- Multiplicity: 48
- Dimension: 1
- Error: 0
\(\textbf{a}=(23,31,26)\)
- Multiplicity: 20
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,21,27)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(20,28,32)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,32,22)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,30,19)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,24,26)\)
- Multiplicity: 47
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,26,29)\)
- Multiplicity: 74
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,21,32)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(18,31,31)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,27,25)\)
- Multiplicity: 93
- Dimension: 1
- Error: 0
\(\textbf{a}=(23,29,28)\)
- Multiplicity: 48
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,19,29)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,24,31)\)
- Multiplicity: 23
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,30,24)\)
- Multiplicity: 47
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,28,21)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(21,32,27)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,22,28)\)
- Multiplicity: 28
- Dimension: 1
- Error: 0
\(\textbf{a}=(23,27,30)\)
- Multiplicity: 37
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,31,20)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,25,27)\)
- Multiplicity: 93
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,20,30)\)
- Multiplicity: 9
- Dimension: 1
- Error: 0
\(\textbf{a}=(21,30,29)\)
- Multiplicity: 16
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,26,23)\)
- Multiplicity: 20
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,28,26)\)
- Multiplicity: 102
- Dimension: 1
- Error: 0
\(\textbf{a}=(23,25,32)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,29,22)\)
- Multiplicity: 30
- Dimension: 1
- Error: 0
\(\textbf{a}=(24,31,25)\)
- Multiplicity: 23
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,23,29)\)
- Multiplicity: 48
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,18,32)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(21,28,31)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,24,25)\)
- Multiplicity: 23
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,30,18)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,32,21)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,26,28)\)
- Multiplicity: 102
- Dimension: 1
- Error: 0
Below is a plot displaying the Schur decomposition. In the \(\lambda=(\lambda_0,\lambda_1)\) spot we place \(\beta_{14,\lambda}(2,0;5)\), the multiplicity of \(\textbf{S}_{\lambda}\) occuring in the decomposition of \(K_{14,2}(2,0;5)\). 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!
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28 |
29 |
30 |
31 |
32 |
33 |
23 |
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24 |
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· |
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· |
2
| · |
25 |
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· |
1
| · |
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26 |
· |
1
| 1
| 3
| 2
| 2
| · |
27 |
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1
| 2
| 2
| 2
| 1
| · |
28 |
· |
2
| 2
| 3
| 2
| 2
| · |
29 |
· |
· |
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1
| 1
| · |
· |
30 |
· |
· |
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1
| 1
| 1
| · |
31 |
· |
· |
· |
· |
· |
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· |
Below is a plot displaying the multigraded Betti numbers. In the \((a_0,a_1)\) spot we place \(\beta_{14,\textbf{a}}(2,0;5)\). 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!