Current Betti Table Entry:
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0 |
1 |
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9 |
10 |
11 |
12 |
0 |
(3,0,0) |
(6,1,0) |
(9,1,1) |
(11,3,1) |
(13,4,2) |
(15,4,4) |
(16,7,4) |
(17,9,5) |
(18,10,7) |
(19,10,10) |
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1 |
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· |
· |
· |
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(15,15,5) |
(17,15,7) |
(18,16,9) |
(19,16,12) |
(19,18,14) |
(19,19,17) |
2 |
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· |
· |
· |
· |
· |
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8 |
9 |
10 |
11 |
12 |
0 |
1 |
3 |
11 |
17 |
21 |
24 |
23 |
19 |
4 |
1 |
· |
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1 |
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· |
· |
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5 |
11 |
11 |
7 |
2 |
1 |
2 |
· |
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1 |
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9 |
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0 |
1 |
3 |
12 |
28 |
46 |
56 |
48 |
25 |
4 |
1 |
· |
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· |
1 |
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5 |
13 |
12 |
7 |
2 |
1 |
2 |
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\(\lambda=(15,14,14)\)
- Multiplicity: 1
- Dimension: 3
- Dominant: No
\(\lambda=(16,14,13)\)
- Multiplicity: 1
- Dimension: 15
- Dominant: No
\(\lambda=(16,16,11)\)
- Multiplicity: 1
- Dimension: 21
- Dominant: No
\(\lambda=(17,14,12)\)
- Multiplicity: 2
- Dimension: 42
- Dominant: No
\(\lambda=(18,14,11)\)
- Multiplicity: 1
- Dimension: 90
- Dominant: No
\(\lambda=(18,16,9)\)
- Multiplicity: 1
- Dimension: 132
- Dominant: Yes
\(\lambda=(17,16,10)\)
- Multiplicity: 1
- Dimension: 63
- Dominant: No
\(\lambda=(16,15,12)\)
- Multiplicity: 1
- Dimension: 24
- Dominant: No
\(\lambda=(18,15,10)\)
- Multiplicity: 1
- Dimension: 120
- Dominant: No
\(\lambda=(18,13,12)\)
- Multiplicity: 1
- Dimension: 48
- Dominant: No
\(\lambda=(17,15,11)\)
- Multiplicity: 1
- Dimension: 60
- Dominant: No
\(\textbf{a}=(14,12,17)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(17,14,12)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(15,18,10)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(12,16,15)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(14,11,18)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(12,15,16)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(17,13,13)\)
- Multiplicity: 12
- Dimension: 1
- Error: 0
\(\textbf{a}=(15,17,11)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(12,14,17)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(15,16,12)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(17,12,14)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(10,18,15)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(12,13,18)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(10,17,16)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(15,15,13)\)
- Multiplicity: 25
- Dimension: 1
- Error: 0
\(\textbf{a}=(17,11,15)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(10,16,17)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(13,18,12)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(18,16,9)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(15,14,14)\)
- Multiplicity: 30
- Dimension: 1
- Error: 0
\(\textbf{a}=(17,10,16)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(10,15,18)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(17,9,17)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(13,17,13)\)
- Multiplicity: 12
- Dimension: 1
- Error: 0
\(\textbf{a}=(18,15,10)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(15,13,15)\)
- Multiplicity: 25
- Dimension: 1
- Error: 0
\(\textbf{a}=(16,18,9)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(18,14,11)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(13,16,14)\)
- Multiplicity: 22
- Dimension: 1
- Error: 0
\(\textbf{a}=(15,12,16)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(15,11,17)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(18,13,12)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(16,17,10)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(13,15,15)\)
- Multiplicity: 25
- Dimension: 1
- Error: 0
\(\textbf{a}=(15,10,18)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(18,12,13)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(16,16,11)\)
- Multiplicity: 10
- Dimension: 1
- Error: 0
\(\textbf{a}=(11,18,14)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(13,14,16)\)
- Multiplicity: 22
- Dimension: 1
- Error: 0
\(\textbf{a}=(13,13,17)\)
- Multiplicity: 12
- Dimension: 1
- Error: 0
\(\textbf{a}=(16,15,12)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(18,11,14)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(11,17,15)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(13,12,18)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(11,16,16)\)
- Multiplicity: 10
- Dimension: 1
- Error: 0
\(\textbf{a}=(16,14,13)\)
- Multiplicity: 22
- Dimension: 1
- Error: 0
\(\textbf{a}=(14,18,11)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(18,10,15)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(11,15,17)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(14,17,12)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(16,13,14)\)
- Multiplicity: 22
- Dimension: 1
- Error: 0
\(\textbf{a}=(18,9,16)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(11,14,18)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(9,18,16)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(14,16,13)\)
- Multiplicity: 22
- Dimension: 1
- Error: 0
\(\textbf{a}=(16,12,15)\)
- Multiplicity: 17
- Dimension: 1
- Error: 0
\(\textbf{a}=(9,17,17)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(17,17,9)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(14,15,14)\)
- Multiplicity: 30
- Dimension: 1
- Error: 0
\(\textbf{a}=(16,11,16)\)
- Multiplicity: 10
- Dimension: 1
- Error: 0
\(\textbf{a}=(9,16,18)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(16,10,17)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(17,16,10)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(12,18,13)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(14,14,15)\)
- Multiplicity: 30
- Dimension: 1
- Error: 0
\(\textbf{a}=(16,9,18)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(17,15,11)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(12,17,14)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(14,13,16)\)
- Multiplicity: 22
- Dimension: 1
- Error: 0
Below is a plot displaying the Schur decomposition. In the \(\lambda=(\lambda_0,\lambda_1)\) spot we place \(\beta_{9,\lambda}(2,3;4)\), the multiplicity of \(\textbf{S}_{\lambda}\) occuring in the decomposition of \(K_{9,1}(2,3;4)\). 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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14 |
15 |
16 |
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18 |
19 |
12 |
· |
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13 |
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1
| · |
14 |
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1
| 1
| 2
| 1
| · |
15 |
· |
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1
| 1
| 1
| · |
16 |
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1
| 1
| 1
| · |
17 |
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· |
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Below is a plot displaying the multigraded Betti numbers. In the \((a_0,a_1)\) spot we place \(\beta_{9,\textbf{a}}(2,3;4)\). 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!