Current Betti Table Entry:
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14 |
15 |
16 |
17 |
18 |
0 |
(4,0,0) |
(8,1,0) |
(12,1,1) |
(15,3,1) |
(18,4,2) |
(21,4,4) |
(23,7,4) |
(25,9,5) |
(27,10,7) |
(29,10,10) |
(30,14,10) |
(31,17,11) |
(32,19,13) |
(33,20,16) |
(34,20,20) |
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1 |
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(24,24,6) |
(27,24,8) |
(29,25,10) |
(31,25,13) |
(32,27,15) |
(33,28,18) |
(34,28,22) |
(34,31,24) |
(34,33,27) |
(34,34,31) |
2 |
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\(\lambda=(33,32,24)\)
- Multiplicity: 1
- Dimension: 99
- Dominant: No
\(\lambda=(34,30,25)\)
- Multiplicity: 1
- Dimension: 165
- Dominant: No
\(\lambda=(32,30,27)\)
- Multiplicity: 1
- Dimension: 42
- Dominant: No
\(\lambda=(31,31,27)\)
- Multiplicity: 1
- Dimension: 15
- Dominant: No
\(\lambda=(34,29,26)\)
- Multiplicity: 1
- Dimension: 120
- Dominant: No
\(\lambda=(33,31,25)\)
- Multiplicity: 2
- Dimension: 105
- Dominant: No
\(\lambda=(32,29,28)\)
- Multiplicity: 1
- Dimension: 24
- Dominant: No
\(\lambda=(34,28,27)\)
- Multiplicity: 1
- Dimension: 63
- Dominant: No
\(\lambda=(33,30,26)\)
- Multiplicity: 1
- Dimension: 90
- Dominant: No
\(\lambda=(31,29,29)\)
- Multiplicity: 1
- Dimension: 6
- Dominant: No
\(\lambda=(33,33,23)\)
- Multiplicity: 1
- Dimension: 66
- Dominant: Yes
\(\lambda=(34,31,24)\)
- Multiplicity: 1
- Dimension: 192
- Dominant: Yes
\(\lambda=(33,29,27)\)
- Multiplicity: 2
- Dimension: 60
- Dominant: No
\(\lambda=(32,31,26)\)
- Multiplicity: 1
- Dimension: 48
- Dominant: No
\(\textbf{a}=(31,24,34)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,28,32)\)
- Multiplicity: 27
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,30,27)\)
- Multiplicity: 22
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,34,25)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,26,29)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,32,30)\)
- Multiplicity: 22
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,27,33)\)
- Multiplicity: 14
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,31,31)\)
- Multiplicity: 27
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,33,26)\)
- Multiplicity: 10
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,29,28)\)
- Multiplicity: 27
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,25,30)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,26,34)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,30,32)\)
- Multiplicity: 22
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,24,31)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,34,30)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,32,27)\)
- Multiplicity: 22
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,28,29)\)
- Multiplicity: 27
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,29,33)\)
- Multiplicity: 14
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,33,31)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,33,23)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,31,28)\)
- Multiplicity: 35
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,27,30)\)
- Multiplicity: 22
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,28,34)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,32,32)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,26,31)\)
- Multiplicity: 15
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,34,27)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,32,24)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,30,29)\)
- Multiplicity: 43
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,31,33)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,25,32)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,31,25)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,33,28)\)
- Multiplicity: 15
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,29,30)\)
- Multiplicity: 43
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,30,34)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,24,33)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,28,31)\)
- Multiplicity: 35
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,34,24)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,30,26)\)
- Multiplicity: 10
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,32,29)\)
- Multiplicity: 27
- Dimension: 1
- Error: 0
\(\textbf{a}=(23,33,33)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,27,32)\)
- Multiplicity: 22
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,29,27)\)
- Multiplicity: 14
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,33,25)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,31,30)\)
- Multiplicity: 35
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,26,33)\)
- Multiplicity: 10
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,30,31)\)
- Multiplicity: 35
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,32,26)\)
- Multiplicity: 15
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,28,28)\)
- Multiplicity: 15
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,34,29)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,25,34)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,29,32)\)
- Multiplicity: 27
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,33,30)\)
- Multiplicity: 10
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,31,27)\)
- Multiplicity: 27
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,27,29)\)
- Multiplicity: 14
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,28,33)\)
- Multiplicity: 15
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,32,31)\)
- Multiplicity: 15
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,34,26)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,30,28)\)
- Multiplicity: 35
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,26,30)\)
- Multiplicity: 10
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,27,34)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,31,32)\)
- Multiplicity: 15
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,25,31)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,33,27)\)
- Multiplicity: 14
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,31,24)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,29,29)\)
- Multiplicity: 40
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,30,33)\)
- Multiplicity: 10
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,24,32)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(24,34,31)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,30,25)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,32,28)\)
- Multiplicity: 27
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,28,30)\)
- Multiplicity: 35
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,29,34)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,23,33)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(24,33,32)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,27,31)\)
- Multiplicity: 27
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,33,24)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,29,26)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,31,29)\)
- Multiplicity: 40
- Dimension: 1
- Error: 0
\(\textbf{a}=(24,32,33)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,26,32)\)
- Multiplicity: 15
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,28,27)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,32,25)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,34,28)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,30,30)\)
- Multiplicity: 43
- Dimension: 1
- Error: 0
\(\textbf{a}=(24,31,34)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,25,33)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,29,31)\)
- Multiplicity: 40
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,27,28)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,31,26)\)
- Multiplicity: 15
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,33,29)\)
- Multiplicity: 14
- Dimension: 1
- Error: 0
Below is a plot displaying the Schur decomposition. In the \(\lambda=(\lambda_0,\lambda_1)\) spot we place \(\beta_{16,\lambda}(2,4;5)\), the multiplicity of \(\textbf{S}_{\lambda}\) occuring in the decomposition of \(K_{16,1}(2,4;5)\). 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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30 |
31 |
32 |
33 |
34 |
35 |
27 |
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28 |
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1
| · |
29 |
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1
| 1
| 2
| 1
| · |
30 |
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1
| 1
| 1
| · |
31 |
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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 \(\beta_{16,\textbf{a}}(2,4;5)\). 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!