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 |
(3,0,0) |
(7,1,0) |
(11,1,1) |
(14,3,1) |
(17,4,2) |
(20,4,4) |
(22,7,4) |
(24,9,5) |
(26,10,7) |
(28,10,10) |
· |
· |
· |
· |
· |
· |
· |
· |
· |
1 |
· |
· |
· |
· |
(14,14,0) |
(18,14,1) |
(21,15,2) |
(24,15,4) |
(26,17,5) |
(28,18,7) |
(30,18,10) |
(31,21,11) |
(32,23,13) |
(33,24,16) |
(34,24,20) |
(34,28,21) |
(34,31,23) |
(34,33,26) |
(34,34,30) |
2 |
· |
· |
· |
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\(\lambda=(32,30,26)\)
- Multiplicity: 1
- Dimension: 60
- Dominant: No
\(\lambda=(34,30,24)\)
- Multiplicity: 1
- Dimension: 210
- Dominant: No
\(\lambda=(33,32,23)\)
- Multiplicity: 1
- Dimension: 120
- Dominant: No
\(\lambda=(33,28,27)\)
- Multiplicity: 1
- Dimension: 48
- Dominant: No
\(\lambda=(30,29,29)\)
- Multiplicity: 1
- Dimension: 3
- Dominant: No
\(\lambda=(31,31,26)\)
- Multiplicity: 1
- Dimension: 21
- Dominant: No
\(\lambda=(32,29,27)\)
- Multiplicity: 2
- Dimension: 42
- Dominant: No
\(\lambda=(34,29,25)\)
- Multiplicity: 2
- Dimension: 165
- Dominant: No
\(\lambda=(33,31,24)\)
- Multiplicity: 2
- Dimension: 132
- Dominant: No
\(\lambda=(31,30,27)\)
- Multiplicity: 1
- Dimension: 24
- Dominant: No
\(\lambda=(34,28,26)\)
- Multiplicity: 1
- Dimension: 105
- Dominant: No
\(\lambda=(33,30,25)\)
- Multiplicity: 2
- Dimension: 120
- Dominant: No
\(\lambda=(31,29,28)\)
- Multiplicity: 1
- Dimension: 15
- Dominant: No
\(\lambda=(33,33,22)\)
- Multiplicity: 1
- Dimension: 78
- Dominant: Yes
\(\lambda=(34,27,27)\)
- Multiplicity: 1
- Dimension: 36
- Dominant: No
\(\lambda=(34,31,23)\)
- Multiplicity: 1
- Dimension: 234
- Dominant: Yes
\(\lambda=(33,29,26)\)
- Multiplicity: 2
- Dimension: 90
- Dominant: No
\(\lambda=(32,31,25)\)
- Multiplicity: 1
- Dimension: 63
- Dominant: No
\(\textbf{a}=(27,32,29)\)
- Multiplicity: 35
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,30,26)\)
- Multiplicity: 26
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,24,33)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,25,29)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,33,25)\)
- Multiplicity: 12
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,27,32)\)
- Multiplicity: 35
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,28,28)\)
- Multiplicity: 37
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,30,31)\)
- Multiplicity: 45
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,25,34)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,31,27)\)
- Multiplicity: 45
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,33,30)\)
- Multiplicity: 12
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,23,31)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,32,23)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,34,26)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,26,30)\)
- Multiplicity: 26
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,28,33)\)
- Multiplicity: 20
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,29,29)\)
- Multiplicity: 67
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,31,32)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,32,28)\)
- Multiplicity: 37
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,30,25)\)
- Multiplicity: 12
- Dimension: 1
- Error: 0
\(\textbf{a}=(23,34,31)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,24,32)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,29,34)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,33,24)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,27,31)\)
- Multiplicity: 45
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,28,27)\)
- Multiplicity: 20
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,30,30)\)
- Multiplicity: 59
- Dimension: 1
- Error: 0
\(\textbf{a}=(23,32,33)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,31,26)\)
- Multiplicity: 31
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,33,29)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,25,33)\)
- Multiplicity: 12
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,26,29)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,34,25)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,28,32)\)
- Multiplicity: 37
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,29,28)\)
- Multiplicity: 54
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,31,31)\)
- Multiplicity: 31
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,26,34)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,32,27)\)
- Multiplicity: 35
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,30,24)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(24,34,30)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,24,31)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,33,23)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,27,30)\)
- Multiplicity: 45
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,29,33)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,30,29)\)
- Multiplicity: 67
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,28,26)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(24,32,32)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,22,33)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,33,28)\)
- Multiplicity: 20
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,31,25)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,25,32)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(24,30,34)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,26,28)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,34,24)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,28,31)\)
- Multiplicity: 54
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,23,34)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,29,27)\)
- Multiplicity: 35
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,31,30)\)
- Multiplicity: 45
- Dimension: 1
- Error: 0
\(\textbf{a}=(22,33,33)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,32,26)\)
- Multiplicity: 26
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,34,29)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,24,30)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,26,33)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,27,29)\)
- Multiplicity: 35
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,33,22)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,29,32)\)
- Multiplicity: 35
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,30,28)\)
- Multiplicity: 59
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,32,31)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,27,34)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,33,27)\)
- Multiplicity: 20
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,31,24)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,25,31)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,34,23)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,28,30)\)
- Multiplicity: 59
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,30,33)\)
- Multiplicity: 12
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,31,29)\)
- Multiplicity: 54
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,29,26)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(23,33,32)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,23,33)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,34,28)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,32,25)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,26,32)\)
- Multiplicity: 26
- Dimension: 1
- Error: 0
\(\textbf{a}=(23,31,34)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,27,28)\)
- Multiplicity: 20
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,29,31)\)
- Multiplicity: 54
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,24,34)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,30,27)\)
- Multiplicity: 45
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,32,30)\)
- Multiplicity: 26
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,31,23)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,33,26)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,25,30)\)
- Multiplicity: 12
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,27,33)\)
- Multiplicity: 20
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,28,29)\)
- Multiplicity: 54
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,30,32)\)
- Multiplicity: 26
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,31,28)\)
- Multiplicity: 54
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,29,25)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(24,33,31)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,23,32)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,28,34)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,34,27)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,32,24)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,26,31)\)
- Multiplicity: 31
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,27,27)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,29,30)\)
- Multiplicity: 67
- Dimension: 1
- Error: 0
\(\textbf{a}=(24,31,33)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
Below is a plot displaying the Schur decomposition. In the \(\lambda=(\lambda_0,\lambda_1)\) spot we place \(\beta_{16,\lambda}(2,3;5)\), the multiplicity of \(\textbf{S}_{\lambda}\) occuring in the decomposition of \(K_{16,1}(2,3;5)\). 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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· |
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27 |
· |
· |
· |
· |
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1
| · |
28 |
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· |
· |
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1
| 1
| · |
29 |
· |
1
| 1
| 2
| 2
| 2
| · |
30 |
· |
· |
1
| 1
| 2
| 1
| · |
31 |
· |
· |
1
| 1
| 2
| 1
| · |
32 |
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1
| · |
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33 |
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1
| · |
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34 |
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Below is a plot displaying the multigraded Betti numbers. In the \((a_0,a_1)\) spot we place \(\beta_{16,\textbf{a}}(2,3;5)\). 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!