Current Betti Table Entry:
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25 |
0 |
(4,0,0) |
(9,1,0) |
(14,1,1) |
(18,3,1) |
(22,4,2) |
(26,4,4) |
? |
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1 |
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(48,30,16) |
(50,30,20) |
(51,34,21) |
(52,37,23) |
(53,39,26) |
(54,40,30) |
(55,40,35) |
(55,45,36) |
(55,49,38) |
(55,52,41) |
(55,54,45) |
(55,55,50) |
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0 |
1 |
4 |
22 |
41 |
60 |
78 |
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1 |
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166 |
160 |
152 |
137 |
123 |
104 |
85 |
67 |
46 |
26 |
5 |
1 |
2 |
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\(\lambda=(55,50,49)\)
- Multiplicity: 1
- Dimension: 48
- Dominant: No
\(\lambda=(55,51,48)\)
- Multiplicity: 1
- Dimension: 90
- Dominant: No
\(\lambda=(55,54,45)\)
- Multiplicity: 1
- Dimension: 120
- Dominant: Yes
\(\lambda=(55,53,46)\)
- Multiplicity: 1
- Dimension: 132
- Dominant: No
\(\lambda=(55,52,47)\)
- Multiplicity: 1
- Dimension: 120
- Dominant: No
\(\textbf{a}=(50,50,54)\)
- Multiplicity: 10
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,52,49)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,48,51)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(48,54,52)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,49,55)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(48,53,53)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,51,50)\)
- Multiplicity: 13
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,55,48)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,47,52)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(48,52,54)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,54,49)\)
- Multiplicity: 9
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,50,51)\)
- Multiplicity: 13
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,46,53)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(48,51,55)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,45,54)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(46,55,53)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,55,45)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,53,50)\)
- Multiplicity: 13
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,49,52)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(46,54,54)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,54,46)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,52,51)\)
- Multiplicity: 15
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,48,53)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
\(\textbf{a}=(46,53,55)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,47,54)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,53,47)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(49,55,50)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,51,52)\)
- Multiplicity: 15
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,46,55)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,50,53)\)
- Multiplicity: 13
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,52,48)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(49,54,51)\)
- Multiplicity: 9
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,49,54)\)
- Multiplicity: 9
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,51,49)\)
- Multiplicity: 9
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,55,47)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(49,53,52)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,48,55)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(49,52,53)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,50,50)\)
- Multiplicity: 10
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,54,48)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(49,51,54)\)
- Multiplicity: 9
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,53,49)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,49,51)\)
- Multiplicity: 9
- Dimension: 1
- Error: 0
\(\textbf{a}=(47,55,52)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(49,50,55)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(47,54,53)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,52,50)\)
- Multiplicity: 14
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,54,45)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,48,52)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(47,53,54)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,55,49)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,53,46)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,51,51)\)
- Multiplicity: 15
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,47,53)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(47,52,55)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,46,54)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,52,47)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,54,50)\)
- Multiplicity: 10
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,50,52)\)
- Multiplicity: 14
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,45,55)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(45,55,54)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,55,46)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,51,48)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,53,51)\)
- Multiplicity: 13
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,49,53)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(45,54,55)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,48,54)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,50,49)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,54,47)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,52,52)\)
- Multiplicity: 14
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,47,55)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,51,53)\)
- Multiplicity: 13
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,49,50)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,53,48)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
\(\textbf{a}=(48,55,51)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
Below is a plot displaying the Schur decomposition. In the \(\lambda=(\lambda_0,\lambda_1)\) spot we place \(\beta_{24,\lambda}(2,4;6)\), the multiplicity of \(\textbf{S}_{\lambda}\) occuring in the decomposition of \(K_{24,1}(2,4;6)\). 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 |
49 |
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50 |
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1
| · |
51 |
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1
| · |
52 |
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1
| · |
53 |
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1
| · |
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 \(\beta_{24,\textbf{a}}(2,4;6)\). 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!