Current Betti Table Entry:
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(0,0,0) |
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(6,2,0) |
(9,2,1) |
(11,4,1) |
(13,5,2) |
(15,5,4) |
(16,8,4) |
(17,10,5) |
(18,11,7) |
(19,11,10) |
(19,14,11) |
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(18,18,12) |
(19,18,15) |
(19,19,18) |
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\(\lambda=(17,14,9)\)
- Multiplicity: 1
- Dimension: 120
- Dominant: No
\(\lambda=(18,12,10)\)
- Multiplicity: 1
- Dimension: 105
- Dominant: No
\(\lambda=(16,16,8)\)
- Multiplicity: 1
- Dimension: 45
- Dominant: No
\(\lambda=(16,12,12)\)
- Multiplicity: 1
- Dimension: 15
- Dominant: No
\(\lambda=(15,14,11)\)
- Multiplicity: 1
- Dimension: 24
- Dominant: No
\(\lambda=(17,13,10)\)
- Multiplicity: 1
- Dimension: 90
- Dominant: No
\(\lambda=(14,14,12)\)
- Multiplicity: 1
- Dimension: 6
- Dominant: No
\(\lambda=(18,14,8)\)
- Multiplicity: 1
- Dimension: 210
- Dominant: Yes
\(\lambda=(17,12,11)\)
- Multiplicity: 1
- Dimension: 48
- Dominant: No
\(\lambda=(16,14,10)\)
- Multiplicity: 2
- Dimension: 60
- Dominant: No
\(\lambda=(19,11,10)\)
- Multiplicity: 1
- Dimension: 99
- Dominant: Yes
\(\lambda=(18,13,9)\)
- Multiplicity: 1
- Dimension: 165
- Dominant: No
\(\lambda=(16,13,11)\)
- Multiplicity: 1
- Dimension: 42
- Dominant: No
\(\textbf{a}=(11,10,19)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(9,14,17)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(16,8,16)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(14,12,14)\)
- Multiplicity: 36
- Dimension: 1
- Error: 0
\(\textbf{a}=(19,10,11)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(17,14,9)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(12,16,12)\)
- Multiplicity: 22
- Dimension: 1
- Error: 0
\(\textbf{a}=(9,13,18)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(14,11,15)\)
- Multiplicity: 24
- Dimension: 1
- Error: 0
\(\textbf{a}=(17,13,10)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
\(\textbf{a}=(15,17,8)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(10,19,11)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(12,15,13)\)
- Multiplicity: 30
- Dimension: 1
- Error: 0
\(\textbf{a}=(14,10,16)\)
- Multiplicity: 13
- Dimension: 1
- Error: 0
\(\textbf{a}=(12,14,14)\)
- Multiplicity: 36
- Dimension: 1
- Error: 0
\(\textbf{a}=(17,12,11)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(15,16,9)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(10,18,12)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(14,9,17)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(12,13,15)\)
- Multiplicity: 30
- Dimension: 1
- Error: 0
\(\textbf{a}=(15,15,10)\)
- Multiplicity: 13
- Dimension: 1
- Error: 0
\(\textbf{a}=(17,11,12)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(10,17,13)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
\(\textbf{a}=(14,8,18)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(12,12,16)\)
- Multiplicity: 22
- Dimension: 1
- Error: 0
\(\textbf{a}=(10,16,14)\)
- Multiplicity: 13
- Dimension: 1
- Error: 0
\(\textbf{a}=(13,18,9)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(15,14,11)\)
- Multiplicity: 24
- Dimension: 1
- Error: 0
\(\textbf{a}=(17,10,13)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
\(\textbf{a}=(12,11,17)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(10,15,15)\)
- Multiplicity: 13
- Dimension: 1
- Error: 0
\(\textbf{a}=(17,9,14)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(13,17,10)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
\(\textbf{a}=(15,13,12)\)
- Multiplicity: 30
- Dimension: 1
- Error: 0
\(\textbf{a}=(12,10,18)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(10,14,16)\)
- Multiplicity: 13
- Dimension: 1
- Error: 0
\(\textbf{a}=(17,8,15)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(8,18,14)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(18,14,8)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(13,16,11)\)
- Multiplicity: 19
- Dimension: 1
- Error: 0
\(\textbf{a}=(15,12,13)\)
- Multiplicity: 30
- Dimension: 1
- Error: 0
\(\textbf{a}=(10,13,17)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
\(\textbf{a}=(8,17,15)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(15,11,14)\)
- Multiplicity: 24
- Dimension: 1
- Error: 0
\(\textbf{a}=(11,19,10)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(18,13,9)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(13,15,12)\)
- Multiplicity: 30
- Dimension: 1
- Error: 0
\(\textbf{a}=(10,12,18)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(8,16,16)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(15,10,15)\)
- Multiplicity: 13
- Dimension: 1
- Error: 0
\(\textbf{a}=(18,12,10)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(16,16,8)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(11,18,11)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(13,14,13)\)
- Multiplicity: 39
- Dimension: 1
- Error: 0
\(\textbf{a}=(10,11,19)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(8,15,17)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(15,9,16)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(13,13,14)\)
- Multiplicity: 39
- Dimension: 1
- Error: 0
\(\textbf{a}=(18,11,11)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(16,15,9)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(11,17,12)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(8,14,18)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(15,8,17)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(13,12,15)\)
- Multiplicity: 30
- Dimension: 1
- Error: 0
\(\textbf{a}=(16,14,10)\)
- Multiplicity: 13
- Dimension: 1
- Error: 0
\(\textbf{a}=(14,18,8)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(18,10,12)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(11,16,13)\)
- Multiplicity: 19
- Dimension: 1
- Error: 0
\(\textbf{a}=(13,11,16)\)
- Multiplicity: 19
- Dimension: 1
- Error: 0
\(\textbf{a}=(11,15,14)\)
- Multiplicity: 24
- Dimension: 1
- Error: 0
\(\textbf{a}=(16,13,11)\)
- Multiplicity: 19
- Dimension: 1
- Error: 0
\(\textbf{a}=(14,17,9)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(18,9,13)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(13,10,17)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
\(\textbf{a}=(11,14,15)\)
- Multiplicity: 24
- Dimension: 1
- Error: 0
\(\textbf{a}=(18,8,14)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(9,18,13)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(14,16,10)\)
- Multiplicity: 13
- Dimension: 1
- Error: 0
\(\textbf{a}=(16,12,12)\)
- Multiplicity: 22
- Dimension: 1
- Error: 0
\(\textbf{a}=(13,9,18)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(11,13,16)\)
- Multiplicity: 19
- Dimension: 1
- Error: 0
\(\textbf{a}=(9,17,14)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(14,15,11)\)
- Multiplicity: 24
- Dimension: 1
- Error: 0
\(\textbf{a}=(16,11,13)\)
- Multiplicity: 19
- Dimension: 1
- Error: 0
\(\textbf{a}=(11,12,17)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(9,16,15)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(16,10,14)\)
- Multiplicity: 13
- Dimension: 1
- Error: 0
\(\textbf{a}=(12,18,10)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(14,14,12)\)
- Multiplicity: 36
- Dimension: 1
- Error: 0
\(\textbf{a}=(11,11,18)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(9,15,16)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(16,9,15)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(17,15,8)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(19,11,10)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(12,17,11)\)
- Multiplicity: 11
- Dimension: 1
- Error: 0
\(\textbf{a}=(14,13,13)\)
- Multiplicity: 39
- Dimension: 1
- Error: 0
Below is a plot displaying the Schur decomposition. In the \(\lambda=(\lambda_0,\lambda_1)\) spot we place \(\beta_{9,\lambda}(2,0;4)\), the multiplicity of \(\textbf{S}_{\lambda}\) occuring in the decomposition of \(K_{9,1}(2,0;4)\). 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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Below is a plot displaying the multigraded Betti numbers. In the \((a_0,a_1)\) spot we place \(\beta_{9,\textbf{a}}(2,0;4)\). 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!