Current Betti Table Entry:
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(1,0,0) |
(5,1,0) |
(9,1,1) |
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(11,5,0) |
(15,5,1) |
(18,6,2) |
(21,6,4) |
(23,9,4) |
(25,11,5) |
(27,12,7) |
(29,12,10) |
(30,16,10) |
(31,19,11) |
(32,21,13) |
(33,22,16) |
(34,22,20) |
(34,26,21) |
(34,29,23) |
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(33,33,25) |
(34,33,29) |
(34,34,33) |
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\(\lambda=(34,27,25)\)
- Multiplicity: 1
- Dimension: 132
- Dominant: No
\(\lambda=(34,29,23)\)
- Multiplicity: 1
- Dimension: 273
- Dominant: Yes
\(\textbf{a}=(24,29,33)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,25,27)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,33,23)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,27,30)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,28,26)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,30,29)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,31,25)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,33,28)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,23,29)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,25,32)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,26,28)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,34,24)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,28,31)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,23,34)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,29,27)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,31,30)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,26,33)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,32,26)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,30,23)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(23,34,29)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,24,30)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,27,29)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,29,32)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,30,28)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,28,25)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(23,32,31)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,27,34)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,33,27)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,31,24)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,25,31)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(23,30,33)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,26,27)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,34,23)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,28,30)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,29,26)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,31,29)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,23,33)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,32,25)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(24,34,28)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,24,29)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,26,32)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,27,28)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,29,31)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,24,34)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,30,27)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,28,24)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(24,32,30)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,27,33)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,33,26)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,31,23)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,25,30)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,26,26)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,28,29)\)
- Multiplicity: 9
- Dimension: 1
- Error: 0
\(\textbf{a}=(24,30,32)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,31,28)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,29,25)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,23,32)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(24,28,34)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,24,28)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,34,27)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,32,24)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,26,31)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,27,27)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,29,30)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,30,26)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,32,29)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,24,33)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,33,25)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,25,29)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,27,32)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,28,28)\)
- Multiplicity: 8
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,30,31)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,25,34)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,31,27)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,29,24)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(23,33,30)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,23,31)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(25,28,33)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,34,26)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,32,23)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,26,30)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,27,26)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,29,29)\)
- Multiplicity: 9
- Dimension: 1
- Error: 0
\(\textbf{a}=(23,31,32)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,30,25)\)
- Multiplicity: 4
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,32,28)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(30,24,32)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(23,29,34)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,25,28)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,33,24)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,27,31)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,28,27)\)
- Multiplicity: 7
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,30,30)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,31,26)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,29,23)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(24,33,29)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(33,23,30)\)
- Multiplicity: 1
- Dimension: 1
- Error: 0
\(\textbf{a}=(28,25,33)\)
- Multiplicity: 3
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,34,25)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,26,29)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,28,32)\)
- Multiplicity: 5
- Dimension: 1
- Error: 0
\(\textbf{a}=(29,29,28)\)
- Multiplicity: 9
- Dimension: 1
- Error: 0
\(\textbf{a}=(34,27,25)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(24,31,31)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(26,26,34)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(27,32,27)\)
- Multiplicity: 6
- Dimension: 1
- Error: 0
\(\textbf{a}=(32,30,24)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
\(\textbf{a}=(31,24,31)\)
- Multiplicity: 2
- Dimension: 1
- Error: 0
Below is a plot displaying the Schur decomposition. In the \(\lambda=(\lambda_0,\lambda_1)\) spot we place \(\beta_{16,\lambda}(2,1;5)\), the multiplicity of \(\textbf{S}_{\lambda}\) occuring in the decomposition of \(K_{16,1}(2,1;5)\). 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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1
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1
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Below is a plot displaying the multigraded Betti numbers. In the \((a_0,a_1)\) spot we place \(\beta_{16,\textbf{a}}(2,1;5)\). 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!