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 |
(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 |
· |
· |
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(34,34,34) |
\(\lambda=(30,29,28)\)
- Multiplicity: 1
- Dimension: 8
- Dominant: No
\(\lambda=(33,31,23)\)
- Multiplicity: 1
- Dimension: 162
- Dominant: No
\(\lambda=(34,29,24)\)
- Multiplicity: 1
- Dimension: 216
- Dominant: No
\(\lambda=(32,29,26)\)
- Multiplicity: 1
- Dimension: 64
- Dominant: No
\(\lambda=(31,30,26)\)
- Multiplicity: 1
- Dimension: 35
- Dominant: No
\(\lambda=(32,28,27)\)
- Multiplicity: 1
- Dimension: 35
- Dominant: No
\(\lambda=(34,28,25)\)
- Multiplicity: 1
- Dimension: 154
- Dominant: No
\(\lambda=(33,30,24)\)
- Multiplicity: 1
- Dimension: 154
- Dominant: No
\(\lambda=(31,29,27)\)
- Multiplicity: 1
- Dimension: 27
- Dominant: No
\(\lambda=(34,27,26)\)
- Multiplicity: 1
- Dimension: 80
- Dominant: No
\(\lambda=(33,29,25)\)
- Multiplicity: 2
- Dimension: 125
- Dominant: No
\(\lambda=(32,31,24)\)
- Multiplicity: 1
- Dimension: 80
- Dominant: No
\(\lambda=(33,32,22)\)
- Multiplicity: 1
- Dimension: 143
- Dominant: Yes
\(\lambda=(34,30,23)\)
- Multiplicity: 1
- Dimension: 260
- Dominant: Yes
\(\lambda=(33,28,26)\)
- Multiplicity: 1
- Dimension: 81
- Dominant: No
\(\lambda=(32,30,25)\)
- Multiplicity: 1
- Dimension: 81
- Dominant: No
\(\textbf{a}=(24,29,34)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,25,28)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,33,24)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,27,31)\)
- Multiplicity: 38
- Dimension: 1
- Error: 0
\(\textbf{a}=(22,32,33)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,28,27)\)
- Multiplicity: 27
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,30,30)\)
- Multiplicity: 42
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,25,33)\)
- Multiplicity: 10
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,31,26)\)
- Multiplicity: 29
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,33,29)\)
- Multiplicity: 10
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,23,30)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,32,22)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,34,25)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,26,29)\)
- Multiplicity: 23
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,28,32)\)
- Multiplicity: 27
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,29,28)\)
- Multiplicity: 51
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,31,31)\)
- Multiplicity: 18
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,26,34)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,32,27)\)
- Multiplicity: 27
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,30,24)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(23,34,30)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,24,31)\)
- Multiplicity: 9
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,29,33)\)
- Multiplicity: 10
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,33,23)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,27,30)\)
- Multiplicity: 42
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,28,26)\)
- Multiplicity: 13
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,30,29)\)
- Multiplicity: 51
- Dimension: 1
- Error: 0
\(\textbf{a}=(23,32,32)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,22,33)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,33,28)\)
- Multiplicity: 13
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,31,25)\)
- Multiplicity: 18
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,25,32)\)
- Multiplicity: 16
- Dimension: 1
- Error: 0
\(\textbf{a}=(23,30,34)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,26,28)\)
- Multiplicity: 13
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,34,24)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,28,31)\)
- Multiplicity: 41
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,23,34)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,29,27)\)
- Multiplicity: 38
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,31,30)\)
- Multiplicity: 29
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,26,33)\)
- Multiplicity: 13
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,32,26)\)
- Multiplicity: 23
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,30,23)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(24,34,29)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,24,30)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,33,22)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,27,29)\)
- Multiplicity: 38
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,29,32)\)
- Multiplicity: 23
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,30,28)\)
- Multiplicity: 51
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,28,25)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(24,32,31)\)
- Multiplicity: 9
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,22,32)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,27,34)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,33,27)\)
- Multiplicity: 14
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,31,24)\)
- Multiplicity: 9
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,25,31)\)
- Multiplicity: 18
- Dimension: 1
- Error: 0
\(\textbf{a}=(24,30,33)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,26,27)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,34,23)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,28,30)\)
- Multiplicity: 51
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,29,26)\)
- Multiplicity: 23
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,31,29)\)
- Multiplicity: 38
- Dimension: 1
- Error: 0
\(\textbf{a}=(22,33,32)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,23,33)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,24,29)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,34,28)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,32,25)\)
- Multiplicity: 16
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,26,32)\)
- Multiplicity: 23
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,27,28)\)
- Multiplicity: 27
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,29,31)\)
- Multiplicity: 38
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,24,34)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,30,27)\)
- Multiplicity: 42
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,32,30)\)
- Multiplicity: 16
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,27,33)\)
- Multiplicity: 14
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,33,26)\)
- Multiplicity: 13
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,31,23)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,25,30)\)
- Multiplicity: 16
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,28,29)\)
- Multiplicity: 51
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,30,32)\)
- Multiplicity: 16
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,31,28)\)
- Multiplicity: 41
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,29,25)\)
- Multiplicity: 10
- Dimension: 1
- Error: 0
\(\textbf{a}=(23,33,31)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,23,32)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,28,34)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,34,27)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,32,24)\)
- Multiplicity: 9
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,26,31)\)
- Multiplicity: 29
- Dimension: 1
- Error: 0
\(\textbf{a}=(23,31,33)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,27,27)\)
- Multiplicity: 14
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,29,30)\)
- Multiplicity: 51
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,30,26)\)
- Multiplicity: 29
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,32,29)\)
- Multiplicity: 23
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,24,33)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,33,25)\)
- Multiplicity: 10
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,25,29)\)
- Multiplicity: 10
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,27,32)\)
- Multiplicity: 27
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,28,28)\)
- Multiplicity: 41
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,30,31)\)
- Multiplicity: 29
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,25,34)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,31,27)\)
- Multiplicity: 38
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,29,24)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(24,33,30)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,23,31)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,28,33)\)
- Multiplicity: 13
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,34,26)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,32,23)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,26,30)\)
- Multiplicity: 29
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,27,26)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,29,29)\)
- Multiplicity: 57
- Dimension: 1
- Error: 0
\(\textbf{a}=(24,31,32)\)
- Multiplicity: 9
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,32,28)\)
- Multiplicity: 27
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,30,25)\)
- Multiplicity: 16
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,24,32)\)
- Multiplicity: 9
- Dimension: 1
- Error: 0
Below is a plot displaying the Schur decomposition. In the \(\lambda=(\lambda_0,\lambda_1)\) spot we place \(\beta_{16,\lambda}(2,2;5)\), the multiplicity of \(\textbf{S}_{\lambda}\) occuring in the decomposition of \(K_{16,1}(2,2;5)\). 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!
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29 |
30 |
31 |
32 |
33 |
34 |
35 |
26 |
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27 |
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1
| · |
28 |
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1
| 1
| 1
| · |
29 |
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1
| 1
| 1
| 2
| 1
| · |
30 |
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1
| 1
| 1
| 1
| · |
31 |
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1
| 1
| · |
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32 |
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1
| · |
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33 |
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Below is a plot displaying the multigraded Betti numbers. In the \((a_0,a_1)\) spot we place \(\beta_{16,\textbf{a}}(2,2;5)\). 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!