Current Betti Table Entry:
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25 |
0 |
(1,0,0) |
(6,1,0) |
(11,1,1) |
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1 |
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(14,5,0) |
(19,5,1) |
(23,6,2) |
(27,6,4) |
(30,9,4) |
(33,11,5) |
(36,12,7) |
(39,12,10) |
(41,16,10) |
(43,19,11) |
(45,21,13) |
(47,22,16) |
(49,22,20) |
(50,27,20) |
(51,31,21) |
(52,34,23) |
(53,36,26) |
(54,37,30) |
(55,37,35) |
(55,42,36) |
(55,46,38) |
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2 |
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(51,51,31) |
(53,51,35) |
(54,52,39) |
(55,52,44) |
(55,54,48) |
(55,55,53) |
\(\lambda=(54,49,48)\)
- Multiplicity: 1
- Dimension: 48
- Dominant: No
\(\lambda=(54,51,46)\)
- Multiplicity: 1
- Dimension: 120
- Dominant: No
\(\lambda=(54,53,44)\)
- Multiplicity: 1
- Dimension: 120
- Dominant: No
\(\lambda=(53,50,48)\)
- Multiplicity: 1
- Dimension: 42
- Dominant: No
\(\lambda=(53,52,46)\)
- Multiplicity: 1
- Dimension: 63
- Dominant: No
\(\lambda=(54,50,47)\)
- Multiplicity: 1
- Dimension: 90
- Dominant: No
\(\lambda=(55,48,48)\)
- Multiplicity: 1
- Dimension: 36
- Dominant: No
\(\lambda=(55,50,46)\)
- Multiplicity: 1
- Dimension: 165
- Dominant: No
\(\lambda=(55,52,44)\)
- Multiplicity: 1
- Dimension: 234
- Dominant: Yes
\(\lambda=(54,54,43)\)
- Multiplicity: 1
- Dimension: 78
- Dominant: Yes
\(\lambda=(54,52,45)\)
- Multiplicity: 1
- Dimension: 132
- Dominant: No
\(\textbf{a}=(48,53,50)\)
- Multiplicity: 19
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,51,47)\)
- Multiplicity: 14
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,45,54)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,46,50)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,54,46)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,48,53)\)
- Multiplicity: 19
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,49,49)\)
- Multiplicity: 20
- Dimension: 1
- Error: 0
\(\textbf{a}=(48,51,52)\)
- Multiplicity: 23
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,46,55)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,52,48)\)
- Multiplicity: 23
- Dimension: 1
- Error: 0
\(\textbf{a}=(46,54,51)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,44,52)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,53,44)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(49,55,47)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,47,51)\)
- Multiplicity: 14
- Dimension: 1
- Error: 0
\(\textbf{a}=(48,49,54)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,50,50)\)
- Multiplicity: 31
- Dimension: 1
- Error: 0
\(\textbf{a}=(46,52,53)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(49,53,49)\)
- Multiplicity: 20
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,51,46)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(44,55,52)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,45,53)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(46,50,55)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,54,45)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,48,52)\)
- Multiplicity: 23
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,49,48)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(49,51,51)\)
- Multiplicity: 28
- Dimension: 1
- Error: 0
\(\textbf{a}=(44,53,54)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,52,47)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(47,54,50)\)
- Multiplicity: 9
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,46,54)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,47,50)\)
- Multiplicity: 9
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,55,46)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(49,49,53)\)
- Multiplicity: 20
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,50,49)\)
- Multiplicity: 27
- Dimension: 1
- Error: 0
\(\textbf{a}=(47,52,52)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(49,47,55)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,53,48)\)
- Multiplicity: 19
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,51,45)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(45,55,51)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,45,52)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,54,44)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,48,51)\)
- Multiplicity: 23
- Dimension: 1
- Error: 0
\(\textbf{a}=(47,50,54)\)
- Multiplicity: 9
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,51,50)\)
- Multiplicity: 31
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,49,47)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(45,53,53)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,43,54)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(48,54,49)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,52,46)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,46,53)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(45,51,55)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,47,49)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,55,45)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,49,52)\)
- Multiplicity: 27
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,44,55)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,50,48)\)
- Multiplicity: 19
- Dimension: 1
- Error: 0
\(\textbf{a}=(48,52,51)\)
- Multiplicity: 23
- Dimension: 1
- Error: 0
\(\textbf{a}=(43,54,54)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,53,47)\)
- Multiplicity: 14
- Dimension: 1
- Error: 0
\(\textbf{a}=(46,55,50)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,45,51)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,47,54)\)
- Multiplicity: 9
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,48,50)\)
- Multiplicity: 19
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,54,43)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(48,50,53)\)
- Multiplicity: 19
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,51,49)\)
- Multiplicity: 28
- Dimension: 1
- Error: 0
\(\textbf{a}=(46,53,52)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(48,48,55)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(49,54,48)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,52,45)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,46,52)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,55,44)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,49,51)\)
- Multiplicity: 28
- Dimension: 1
- Error: 0
\(\textbf{a}=(46,51,54)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(49,52,50)\)
- Multiplicity: 27
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,50,47)\)
- Multiplicity: 9
- Dimension: 1
- Error: 0
\(\textbf{a}=(44,54,53)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,44,54)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(47,55,49)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,53,46)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,47,53)\)
- Multiplicity: 14
- Dimension: 1
- Error: 0
\(\textbf{a}=(44,52,55)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,48,49)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(49,50,52)\)
- Multiplicity: 27
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,45,55)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,51,48)\)
- Multiplicity: 23
- Dimension: 1
- Error: 0
\(\textbf{a}=(47,53,51)\)
- Multiplicity: 14
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,52,44)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,54,47)\)
- Multiplicity: 9
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,46,51)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(49,48,54)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,49,50)\)
- Multiplicity: 27
- Dimension: 1
- Error: 0
\(\textbf{a}=(47,51,53)\)
- Multiplicity: 14
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,52,49)\)
- Multiplicity: 27
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,50,46)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(45,54,52)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,44,53)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(47,49,55)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(48,55,48)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,53,45)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,47,52)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,48,48)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,50,51)\)
- Multiplicity: 31
- Dimension: 1
- Error: 0
\(\textbf{a}=(45,52,54)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
Below is a plot displaying the Schur decomposition. In the \(\lambda=(\lambda_0,\lambda_1)\) spot we place \(\beta_{23,\lambda}(2,1;6)\), the multiplicity of \(\textbf{S}_{\lambda}\) occuring in the decomposition of \(K_{23,2}(2,1;6)\). 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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52 |
53 |
54 |
55 |
56 |
47 |
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48 |
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1
| · |
49 |
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1
| · |
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50 |
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1
| 1
| 1
| · |
51 |
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1
| · |
· |
52 |
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1
| 1
| 1
| · |
53 |
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1
| · |
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54 |
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· |
1
| · |
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55 |
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· |
· |
· |
Below is a plot displaying the multigraded Betti numbers. In the \((a_0,a_1)\) spot we place \(\beta_{23,\textbf{a}}(2,1;6)\). 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!