Current Betti Table Entry:
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0 |
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18 |
19 |
20 |
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22 |
23 |
24 |
25 |
0 |
(0,0,0) |
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· |
· |
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· |
· |
· |
· |
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· |
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· |
· |
· |
· |
· |
· |
· |
1 |
· |
(10,2,0) |
(15,2,1) |
(19,4,1) |
(23,5,2) |
(27,5,4) |
(30,8,4) |
(33,10,5) |
(36,11,7) |
(39,11,10) |
(41,15,10) |
(43,18,11) |
(45,20,13) |
(47,21,16) |
(49,21,20) |
(50,26,20) |
(51,30,21) |
(52,33,23) |
(53,35,26) |
(54,36,30) |
(55,36,35) |
(55,41,36) |
· |
· |
· |
· |
2 |
· |
· |
· |
· |
· |
· |
· |
· |
· |
· |
· |
· |
· |
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· |
· |
(45,45,18) |
(48,45,21) |
(50,46,24) |
(52,46,28) |
(53,48,31) |
(54,49,35) |
(55,49,40) |
(55,52,43) |
(55,54,47) |
(55,55,52) |
\(\lambda=(53,51,46)\)
- Multiplicity: 1
- Dimension: 81
- Dominant: No
\(\lambda=(55,51,44)\)
- Multiplicity: 1
- Dimension: 260
- Dominant: No
\(\lambda=(54,53,43)\)
- Multiplicity: 1
- Dimension: 143
- Dominant: No
\(\lambda=(54,49,47)\)
- Multiplicity: 1
- Dimension: 81
- Dominant: No
\(\lambda=(52,52,46)\)
- Multiplicity: 1
- Dimension: 28
- Dominant: No
\(\lambda=(53,50,47)\)
- Multiplicity: 1
- Dimension: 64
- Dominant: No
\(\lambda=(55,50,45)\)
- Multiplicity: 1
- Dimension: 216
- Dominant: No
\(\lambda=(54,52,44)\)
- Multiplicity: 2
- Dimension: 162
- Dominant: No
\(\lambda=(54,48,48)\)
- Multiplicity: 1
- Dimension: 28
- Dominant: No
\(\lambda=(53,49,48)\)
- Multiplicity: 1
- Dimension: 35
- Dominant: No
\(\lambda=(55,49,46)\)
- Multiplicity: 1
- Dimension: 154
- Dominant: No
\(\lambda=(54,51,45)\)
- Multiplicity: 1
- Dimension: 154
- Dominant: No
\(\lambda=(52,50,48)\)
- Multiplicity: 1
- Dimension: 27
- Dominant: No
\(\lambda=(53,52,45)\)
- Multiplicity: 1
- Dimension: 80
- Dominant: No
\(\lambda=(54,54,42)\)
- Multiplicity: 1
- Dimension: 91
- Dominant: Yes
\(\lambda=(55,48,47)\)
- Multiplicity: 1
- Dimension: 80
- Dominant: No
\(\lambda=(55,52,43)\)
- Multiplicity: 1
- Dimension: 280
- Dominant: Yes
\(\lambda=(54,50,46)\)
- Multiplicity: 2
- Dimension: 125
- Dominant: No
\(\textbf{a}=(48,53,49)\)
- Multiplicity: 34
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,51,46)\)
- Multiplicity: 22
- Dimension: 1
- Error: 0
\(\textbf{a}=(43,55,52)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,45,53)\)
- Multiplicity: 15
- Dimension: 1
- Error: 0
\(\textbf{a}=(45,50,55)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,46,49)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,54,45)\)
- Multiplicity: 10
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,48,52)\)
- Multiplicity: 47
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,43,55)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(43,53,54)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,49,48)\)
- Multiplicity: 34
- Dimension: 1
- Error: 0
\(\textbf{a}=(48,51,51)\)
- Multiplicity: 50
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,46,54)\)
- Multiplicity: 14
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,52,47)\)
- Multiplicity: 37
- Dimension: 1
- Error: 0
\(\textbf{a}=(46,54,50)\)
- Multiplicity: 14
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,44,51)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,53,43)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(49,55,46)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,47,50)\)
- Multiplicity: 29
- Dimension: 1
- Error: 0
\(\textbf{a}=(48,49,53)\)
- Multiplicity: 34
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,50,49)\)
- Multiplicity: 58
- Dimension: 1
- Error: 0
\(\textbf{a}=(46,52,52)\)
- Multiplicity: 27
- Dimension: 1
- Error: 0
\(\textbf{a}=(48,47,55)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(49,53,48)\)
- Multiplicity: 34
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,51,45)\)
- Multiplicity: 10
- Dimension: 1
- Error: 0
\(\textbf{a}=(44,55,51)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,45,52)\)
- Multiplicity: 15
- Dimension: 1
- Error: 0
\(\textbf{a}=(46,50,54)\)
- Multiplicity: 14
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,54,44)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,48,51)\)
- Multiplicity: 50
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,43,54)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(44,53,53)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,49,47)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(49,51,50)\)
- Multiplicity: 58
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,52,46)\)
- Multiplicity: 27
- Dimension: 1
- Error: 0
\(\textbf{a}=(47,54,49)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,46,53)\)
- Multiplicity: 22
- Dimension: 1
- Error: 0
\(\textbf{a}=(44,51,55)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,47,49)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,55,45)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(49,49,52)\)
- Multiplicity: 50
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,44,55)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(42,54,54)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,50,48)\)
- Multiplicity: 47
- Dimension: 1
- Error: 0
\(\textbf{a}=(47,52,51)\)
- Multiplicity: 37
- Dimension: 1
- Error: 0
\(\textbf{a}=(49,47,54)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,53,47)\)
- Multiplicity: 29
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,51,44)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(45,55,50)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,45,51)\)
- Multiplicity: 10
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,54,43)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,48,50)\)
- Multiplicity: 47
- Dimension: 1
- Error: 0
\(\textbf{a}=(47,50,53)\)
- Multiplicity: 29
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,51,49)\)
- Multiplicity: 58
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,49,46)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(45,53,52)\)
- Multiplicity: 15
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,43,53)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(47,48,55)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(48,54,48)\)
- Multiplicity: 19
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,52,45)\)
- Multiplicity: 15
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,46,52)\)
- Multiplicity: 27
- Dimension: 1
- Error: 0
\(\textbf{a}=(45,51,54)\)
- Multiplicity: 10
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,47,48)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,55,44)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,49,51)\)
- Multiplicity: 58
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,44,54)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(43,54,53)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,50,47)\)
- Multiplicity: 29
- Dimension: 1
- Error: 0
\(\textbf{a}=(48,52,50)\)
- Multiplicity: 47
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,53,46)\)
- Multiplicity: 22
- Dimension: 1
- Error: 0
\(\textbf{a}=(46,55,49)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,45,50)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,47,53)\)
- Multiplicity: 29
- Dimension: 1
- Error: 0
\(\textbf{a}=(43,52,55)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,48,49)\)
- Multiplicity: 34
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,54,42)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(48,50,52)\)
- Multiplicity: 47
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,45,55)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,51,48)\)
- Multiplicity: 50
- Dimension: 1
- Error: 0
\(\textbf{a}=(46,53,51)\)
- Multiplicity: 22
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,43,52)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(48,48,54)\)
- Multiplicity: 19
- Dimension: 1
- Error: 0
\(\textbf{a}=(49,54,47)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,52,44)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,46,51)\)
- Multiplicity: 22
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,55,43)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,49,50)\)
- Multiplicity: 58
- Dimension: 1
- Error: 0
\(\textbf{a}=(46,51,53)\)
- Multiplicity: 22
- Dimension: 1
- Error: 0
\(\textbf{a}=(49,52,49)\)
- Multiplicity: 50
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,50,46)\)
- Multiplicity: 14
- Dimension: 1
- Error: 0
\(\textbf{a}=(44,54,52)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,44,53)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
\(\textbf{a}=(46,49,55)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(47,55,48)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,53,45)\)
- Multiplicity: 15
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,47,52)\)
- Multiplicity: 37
- Dimension: 1
- Error: 0
\(\textbf{a}=(44,52,54)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,48,48)\)
- Multiplicity: 19
- Dimension: 1
- Error: 0
\(\textbf{a}=(49,50,51)\)
- Multiplicity: 58
- Dimension: 1
- Error: 0
\(\textbf{a}=(51,45,54)\)
- Multiplicity: 10
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,51,47)\)
- Multiplicity: 37
- Dimension: 1
- Error: 0
\(\textbf{a}=(47,53,50)\)
- Multiplicity: 29
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,52,43)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,54,46)\)
- Multiplicity: 14
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,46,50)\)
- Multiplicity: 14
- Dimension: 1
- Error: 0
\(\textbf{a}=(49,48,53)\)
- Multiplicity: 34
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,49,49)\)
- Multiplicity: 50
- Dimension: 1
- Error: 0
\(\textbf{a}=(47,51,52)\)
- Multiplicity: 37
- Dimension: 1
- Error: 0
\(\textbf{a}=(49,46,55)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,52,48)\)
- Multiplicity: 47
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,50,45)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(45,54,51)\)
- Multiplicity: 10
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,44,52)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(47,49,54)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(48,55,47)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(53,53,44)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
\(\textbf{a}=(52,47,51)\)
- Multiplicity: 37
- Dimension: 1
- Error: 0
\(\textbf{a}=(54,42,54)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(55,48,47)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(50,50,50)\)
- Multiplicity: 63
- Dimension: 1
- Error: 0
\(\textbf{a}=(45,52,53)\)
- Multiplicity: 15
- Dimension: 1
- Error: 0
Below is a plot displaying the Schur decomposition. In the \(\lambda=(\lambda_0,\lambda_1)\) spot we place \(\beta_{23,\lambda}(2,0;6)\), the multiplicity of \(\textbf{S}_{\lambda}\) occuring in the decomposition of \(K_{23,2}(2,0;6)\). 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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51 |
52 |
53 |
54 |
55 |
56 |
47 |
· |
· |
· |
· |
· |
· |
48 |
· |
· |
· |
1
| 1
| · |
49 |
· |
· |
1
| 1
| 1
| · |
50 |
· |
1
| 1
| 2
| 1
| · |
51 |
· |
· |
1
| 1
| 1
| · |
52 |
· |
1
| 1
| 2
| 1
| · |
53 |
· |
· |
· |
1
| · |
· |
54 |
· |
· |
· |
1
| · |
· |
55 |
· |
· |
· |
· |
· |
· |
Below is a plot displaying the multigraded Betti numbers. In the \((a_0,a_1)\) spot we place \(\beta_{23,\textbf{a}}(2,0;6)\). 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!