Current Betti Table Entry:
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0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
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) |
· |
· |
· |
1 |
· |
· |
· |
· |
· |
· |
· |
(15,15,5) |
(17,15,7) |
(18,16,9) |
(19,16,12) |
(19,18,14) |
(19,19,17) |
2 |
· |
· |
· |
· |
· |
· |
· |
· |
· |
· |
· |
· |
· |
|
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
0 |
1 |
3 |
11 |
17 |
21 |
24 |
23 |
19 |
4 |
1 |
· |
· |
· |
1 |
· |
· |
· |
· |
· |
· |
· |
5 |
11 |
11 |
7 |
2 |
1 |
2 |
· |
· |
· |
· |
· |
· |
· |
· |
· |
· |
· |
· |
· |
|
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
0 |
1 |
3 |
12 |
28 |
46 |
56 |
48 |
25 |
4 |
1 |
· |
· |
· |
1 |
· |
· |
· |
· |
· |
· |
· |
5 |
13 |
12 |
7 |
2 |
1 |
2 |
· |
· |
· |
· |
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\(\lambda=(19,10,10)\)
- Multiplicity: 1
- Dimension: 55
- Dominant: Yes
\(\textbf{a}=(10,19,10)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(12,15,12)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(14,11,14)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(10,18,11)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(17,12,10)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(12,14,13)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(14,10,15)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(17,11,11)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(10,17,12)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(12,13,14)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(17,10,12)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(15,14,10)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(10,16,13)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(12,12,15)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(15,13,11)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(10,15,14)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(12,11,16)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(12,10,17)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(15,12,12)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(13,16,10)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(10,14,15)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(10,13,16)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(13,15,11)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(15,11,13)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(10,12,17)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(13,14,12)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(11,18,10)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(15,10,14)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(10,11,18)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(11,17,11)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(18,11,10)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(13,13,13)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(10,10,19)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(18,10,11)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(11,16,12)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(13,12,14)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(16,13,10)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(11,15,13)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(13,11,15)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(16,12,11)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(11,14,14)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(13,10,16)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(16,11,12)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(14,15,10)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(11,13,15)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(14,14,11)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(16,10,13)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(11,12,16)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(11,11,17)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(14,13,12)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(12,17,10)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(11,10,18)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(12,16,11)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(19,10,10)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(14,12,13)\)
- Multiplicity: 1
- 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 \(K_{9,0}(2,3;4)\). 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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18 |
19 |
20 |
9 |
· |
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· |
10 |
· |
1
| · |
11 |
· |
· |
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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!
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10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
19 |
20 |
10 |
1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| · |
11 |
1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| · |
· |
12 |
1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| · |
· |
· |
13 |
1
| 1
| 1
| 1
| 1
| 1
| 1
| · |
· |
· |
· |
14 |
1
| 1
| 1
| 1
| 1
| 1
| · |
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· |
· |
· |
15 |
1
| 1
| 1
| 1
| 1
| · |
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· |
· |
· |
· |
16 |
1
| 1
| 1
| 1
| · |
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· |
· |
· |
· |
17 |
1
| 1
| 1
| · |
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· |
· |
· |
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18 |
1
| 1
| · |
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· |
· |
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· |
· |
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19 |
1
| · |
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20 |
· |
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