Current Betti Table Entry:
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(3,0,0) |
(8,1,0) |
(13,1,1) |
(17,3,1) |
(21,4,2) |
(25,4,4) |
(28,7,4) |
(31,9,5) |
(34,10,7) |
(37,10,10) |
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(19,14,0) |
(24,14,1) |
(28,15,2) |
(32,15,4) |
(35,17,5) |
(38,18,7) |
(41,18,10) |
(43,21,11) |
(45,23,13) |
(47,24,16) |
(49,24,20) |
(50,29,20) |
(51,33,21) |
(52,36,23) |
(53,38,26) |
(54,39,30) |
(55,39,35) |
(55,44,36) |
(55,48,38) |
(55,51,41) |
(55,53,45) |
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(55,55,55) |
\(\lambda=(55,49,49)\)
- Multiplicity: 1
- Dimension: 28
- Dominant: No
\(\lambda=(55,51,47)\)
- Multiplicity: 1
- Dimension: 125
- Dominant: No
\(\lambda=(55,53,45)\)
- Multiplicity: 1
- Dimension: 162
- Dominant: Yes
\(\textbf{a}=(52,46,55)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,50,53)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,52,48)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,48,50)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(48,54,51)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,49,54)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(48,53,52)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,51,49)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,55,47)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,47,51)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,48,55)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(48,52,53)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,54,48)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,50,50)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,46,52)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(48,51,54)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,45,53)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(46,55,52)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,53,49)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,49,51)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(48,50,55)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(46,54,53)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,54,45)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,52,50)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,48,52)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(46,53,54)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,47,53)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,53,46)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(49,55,49)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,51,51)\)
- Multiplicity: 9
- Dimension: 1
- Error: 0
\(\textbf{a}=(46,52,55)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,46,54)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,52,47)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(49,54,50)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,50,52)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,45,55)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,49,53)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,51,48)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,55,46)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(49,53,51)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,48,54)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(49,52,52)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,50,49)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,54,47)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,47,55)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(49,51,53)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,53,48)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,49,50)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(47,55,51)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(49,50,54)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(47,54,52)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,52,49)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,48,51)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(49,49,55)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(47,53,53)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,55,48)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,53,45)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,51,50)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,47,52)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(47,52,54)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,46,53)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,54,49)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,52,46)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,50,51)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
\(\textbf{a}=(47,51,55)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,45,54)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(45,55,53)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,55,45)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,51,47)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,53,50)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,49,52)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(45,54,54)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,48,53)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,50,48)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,54,46)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,52,51)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
\(\textbf{a}=(45,53,55)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,47,54)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,49,49)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,53,47)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(48,55,50)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,51,52)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
Below is a plot displaying the Schur decomposition. In the \(\lambda=(\lambda_0,\lambda_1)\) spot we place \(\beta_{24,\lambda}(2,3;6)\), the multiplicity of \(\textbf{S}_{\lambda}\) occuring in the decomposition of \(K_{24,1}(2,3;6)\). 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 |
48 |
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49 |
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1
| · |
50 |
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51 |
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1
| · |
52 |
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53 |
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1
| · |
54 |
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Below is a plot displaying the multigraded Betti numbers. In the \((a_0,a_1)\) spot we place \(\beta_{24,\textbf{a}}(2,3;6)\). 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!