Current Betti Table Entry:
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0 |
1 |
2 |
3 |
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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) |
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· |
· |
2 |
· |
· |
· |
· |
· |
· |
· |
· |
· |
· |
· |
· |
· |
(30,30,15) |
(32,30,18) |
(33,31,21) |
(34,31,25) |
(34,33,28) |
(34,34,32) |
\(\lambda=(33,32,25)\)
- Multiplicity: 1
- Dimension: 80
- Dominant: No
\(\lambda=(33,30,27)\)
- Multiplicity: 1
- Dimension: 64
- Dominant: No
\(\lambda=(32,29,29)\)
- Multiplicity: 1
- Dimension: 10
- Dominant: No
\(\lambda=(32,31,27)\)
- Multiplicity: 1
- Dimension: 35
- Dominant: No
\(\lambda=(33,29,28)\)
- Multiplicity: 1
- Dimension: 35
- Dominant: No
\(\lambda=(33,33,24)\)
- Multiplicity: 1
- Dimension: 55
- Dominant: Yes
\(\lambda=(34,29,27)\)
- Multiplicity: 1
- Dimension: 81
- Dominant: No
\(\lambda=(34,31,25)\)
- Multiplicity: 1
- Dimension: 154
- Dominant: Yes
\(\lambda=(33,31,26)\)
- Multiplicity: 1
- Dimension: 81
- Dominant: No
\(\textbf{a}=(29,28,33)\)
- Multiplicity: 9
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,30,28)\)
- Multiplicity: 14
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,34,26)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,26,30)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,32,31)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,27,34)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,31,32)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,33,27)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,29,29)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,25,31)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,30,33)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,34,31)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,32,28)\)
- Multiplicity: 14
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,28,30)\)
- Multiplicity: 14
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,29,34)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,33,32)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,33,24)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,31,29)\)
- Multiplicity: 21
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,27,31)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,32,33)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,26,32)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,34,28)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,32,25)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,30,30)\)
- Multiplicity: 22
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,31,34)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,25,33)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,31,26)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,33,29)\)
- Multiplicity: 9
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,29,31)\)
- Multiplicity: 21
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,28,32)\)
- Multiplicity: 14
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,34,25)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,30,27)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,32,30)\)
- Multiplicity: 14
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,27,33)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,29,28)\)
- Multiplicity: 9
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,33,26)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,31,31)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,26,34)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,30,32)\)
- Multiplicity: 14
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,32,27)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,28,29)\)
- Multiplicity: 9
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,34,30)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,29,33)\)
- Multiplicity: 9
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,33,31)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,31,28)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,27,30)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,28,34)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,32,32)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,34,27)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,30,29)\)
- Multiplicity: 21
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,26,31)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,31,33)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,25,32)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,33,28)\)
- Multiplicity: 9
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,31,25)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,29,30)\)
- Multiplicity: 21
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,30,34)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,24,33)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,30,26)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,32,29)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,28,31)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(24,33,33)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,27,32)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,33,25)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,29,27)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,31,30)\)
- Multiplicity: 21
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,26,33)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,28,28)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,32,26)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,34,29)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,30,31)\)
- Multiplicity: 21
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,25,34)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,29,32)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,27,29)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,31,27)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,33,30)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
Below is a plot displaying the Schur decomposition. In the \(\lambda=(\lambda_0,\lambda_1)\) spot we place \(\beta_{16,\lambda}(2,0;5)\), the multiplicity of \(\textbf{S}_{\lambda}\) occuring in the decomposition of \(K_{16,2}(2,0;5)\). 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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31 |
32 |
33 |
34 |
35 |
28 |
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29 |
· |
1
| 1
| 1
| · |
30 |
· |
· |
1
| · |
· |
31 |
· |
1
| 1
| 1
| · |
32 |
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· |
1
| · |
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33 |
· |
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1
| · |
· |
34 |
· |
· |
· |
· |
· |
Below is a plot displaying the multigraded Betti numbers. In the \((a_0,a_1)\) spot we place \(\beta_{16,\textbf{a}}(2,0;5)\). 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!