Current Betti Table Entry:
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22 |
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24 |
25 |
0 |
(2,0,0) |
(7,1,0) |
(12,1,1) |
(16,3,1) |
(20,4,2) |
(24,4,4) |
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1 |
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(17,9,0) |
(22,9,1) |
(26,10,2) |
(30,10,4) |
(33,12,5) |
(36,13,7) |
(39,13,10) |
(41,17,10) |
(43,20,11) |
(45,22,13) |
(47,23,16) |
(49,23,20) |
(50,28,20) |
(51,32,21) |
(52,35,23) |
(53,37,26) |
(54,38,30) |
(55,38,35) |
(55,43,36) |
(55,47,38) |
(55,50,41) |
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2 |
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(54,54,44) |
(55,54,49) |
(55,55,54) |
\(\lambda=(55,54,49)\)
- Multiplicity: 1
- Dimension: 48
- Dominant: Yes
\(\textbf{a}=(52,54,52)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,52,53)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,50,54)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,49,55)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,55,52)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,53,53)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,51,54)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,50,55)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,54,49)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,54,53)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,52,54)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,51,55)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,53,54)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,53,50)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,55,49)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,55,53)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,52,55)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,54,54)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,54,50)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,52,51)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,53,55)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(49,55,54)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,51,52)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,53,51)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,55,50)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(49,54,55)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,52,52)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,54,51)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,50,53)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,53,52)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,55,51)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,51,53)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,49,54)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
Below is a plot displaying the Schur decomposition. In the \(\lambda=(\lambda_0,\lambda_1)\) spot we place \(\beta_{24,\lambda}(2,2;6)\), the multiplicity of \(\textbf{S}_{\lambda}\) occuring in the decomposition of \(K_{24,2}(2,2;6)\). 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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54 |
55 |
56 |
53 |
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54 |
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1
| · |
55 |
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Below is a plot displaying the multigraded Betti numbers. In the \((a_0,a_1)\) spot we place \(\beta_{24,\textbf{a}}(2,2;6)\). 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!
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49 |
50 |
51 |
52 |
53 |
54 |
55 |
56 |
49 |
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1
| 1
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50 |
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1
| 2
| 1
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51 |
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1
| 2
| 2
| 1
| · |
52 |
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1
| 2
| 2
| 2
| 1
| · |
53 |
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1
| 2
| 2
| 2
| 2
| 1
| · |
54 |
1
| 2
| 2
| 2
| 2
| 2
| 1
| · |
55 |
1
| 1
| 1
| 1
| 1
| 1
| · |
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56 |
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