Matroid 3.12.4272423
| Label | 3.12.4272423 |
|---|---|
| Id | r3_n12_0******0******0***0******0****************0*******0*********************0*******************************0**************0**************************0*0********0***************************************0***0***********0****** |
| Rank | 3 |
| n | 12 |
Basic invariants
Representability
| Characteristic set | characteristic 0 and all primes [0] |
|---|---|
| Realizable | yes |
| Realizable char0 | yes |
| Regular | no |
| Binary | no |
| Ternary | no |
| Quaternary | no |
| Graphic | no |
Realization space
Geometry
Other
| Char poly splits | false |
|---|---|
| Simplicial arrangement | no |
| Realization space: n qbar components | not computed |
Tutte polynomial
\(T = x_{0}^{3} + 9 x_{0}^{2} + 16 x_{0} x_{1} + 29 x_{0} + x_{1}^{9} + 3 x_{1}^{8} + 6 x_{1}^{7} + 10 x_{1}^{6} + 15 x_{1}^{5} + 21 x_{1}^{4} + 28 x_{1}^{3} + 36 x_{1}^{2} + 29 x_{1}\)
Realization space
| Ring | \(\mathbb{Z}[x_{1}]\) |
|---|---|
| Defining ideal | \(\left(49 x_{1}^{2} - 58 x_{1} + 17\right)\) |
| Inequations | \(x_{1} \neq 0\), \(49 x_{1} - 37 \neq 0\), \(7 x_{1} - 5 \neq 0\), \(9 x_{1} - 5 \neq 0\), \(343 x_{1}^{3} - 504 x_{1}^{2} + 221 x_{1} - 20 \neq 0\), \(49 x_{1} - 33 \neq 0\), \(x_{1} - 1 \neq 0\), \(2107 x_{1}^{3} - 3033 x_{1}^{2} + 1377 x_{1} - 195 \neq 0\), \(2401 x_{1}^{4} - 2940 x_{1}^{3} + 753 x_{1}^{2} + 110 x_{1} - 20 \neq 0\), \(2401 x_{1}^{4} - 6713 x_{1}^{3} + 6689 x_{1}^{2} - 2675 x_{1} + 330 \neq 0\), \(49 x_{1}^{2} - 30 x_{1} + 5 \neq 0\), \(2 \neq 0\), \(2156 x_{1}^{3} - 2503 x_{1}^{2} + 666 x_{1} + 33 \neq 0\), \(49 x_{1}^{2} - 86 x_{1} + 33 \neq 0\), \(2107 x_{1}^{3} - 2935 x_{1}^{2} + 1213 x_{1} - 129 \neq 0\), \(2401 x_{1}^{4} - 5341 x_{1}^{3} + 3497 x_{1}^{2} - 551 x_{1} - 86 \neq 0\), \(49 x_{1}^{2} - 100 x_{1} + 43 \neq 0\), \(49 x_{1}^{2} - 37 x_{1} + 4 \neq 0\), \(245 x_{1} - 157 \neq 0\), \(245 x_{1}^{2} - 220 x_{1} + 39 \neq 0\), \(2401 x_{1}^{3} - 6027 x_{1}^{2} + 4995 x_{1} - 1353 \neq 0\), \(2401 x_{1}^{4} - 6027 x_{1}^{3} + 5191 x_{1}^{2} - 1681 x_{1} + 132 \neq 0\), \(12005 x_{1}^{3} - 15876 x_{1}^{2} + 5353 x_{1} - 66 \neq 0\), \(12005 x_{1}^{3} - 19061 x_{1}^{2} + 9515 x_{1} - 1419 \neq 0\), \(2401 x_{1}^{3} - 5341 x_{1}^{2} + 3595 x_{1} - 751 \neq 0\), \(2401 x_{1}^{3} - 2940 x_{1}^{2} + 753 x_{1} + 82 \neq 0\), \(49 x_{1}^{2} - 23 x_{1} - 2 \neq 0\), \(2401 x_{1}^{4} - 2940 x_{1}^{3} + 949 x_{1}^{2} - 10 x_{1} - 8 \neq 0\), \(12005 x_{1}^{4} - 13328 x_{1}^{3} + 3121 x_{1}^{2} + 318 x_{1} - 4 \neq 0\), \(12005 x_{1}^{4} - 16415 x_{1}^{3} + 6481 x_{1}^{2} - 449 x_{1} - 86 \neq 0\), \(98 x_{1}^{2} - 67 x_{1} + 1 \neq 0\), \(98 x_{1}^{3} - 67 x_{1}^{2} - x_{1} + 2 \neq 0\), \(245 x_{1}^{2} - 94 x_{1} - 39 \neq 0\), \(441 x_{1}^{2} - 228 x_{1} - 37 \neq 0\), \(441 x_{1}^{3} - 228 x_{1}^{2} - 41 x_{1} + 4 \neq 0\), \(7 x_{1} - 3 \neq 0\), \(441 x_{1} - 277 \neq 0\), \(196 x_{1}^{2} - 183 x_{1} + 39 \neq 0\), \(245 x_{1}^{2} - 276 x_{1} + 79 \neq 0\), \(21609 x_{1}^{4} - 57673 x_{1}^{3} + 45977 x_{1}^{2} - 11155 x_{1} - 198 \neq 0\), \(2401 x_{1}^{3} - 2842 x_{1}^{2} + 861 x_{1} - 20 \neq 0\), \(49 x_{1}^{2} - 30 x_{1} + 3 \neq 0\), \(21609 x_{1}^{4} - 23716 x_{1}^{3} + 5489 x_{1}^{2} + 526 x_{1} + 12 \neq 0\), \(2401 x_{1}^{4} - 2940 x_{1}^{3} + 655 x_{1}^{2} + 274 x_{1} - 86 \neq 0\), \(9604 x_{1}^{4} - 13475 x_{1}^{3} + 5728 x_{1}^{2} - 559 x_{1} - 66 \neq 0\), \(1372 x_{1}^{3} - 2261 x_{1}^{2} + 1160 x_{1} - 183 \neq 0\), \(9604 x_{1}^{4} - 29253 x_{1}^{3} + 29451 x_{1}^{2} - 11991 x_{1} + 1677 \neq 0\), \(343 x_{1}^{3} - 602 x_{1}^{2} + 385 x_{1} - 86 \neq 0\), \(21609 x_{1}^{3} - 58359 x_{1}^{2} + 47475 x_{1} - 12133 \neq 0\), \(3087 x_{1}^{3} - 4144 x_{1}^{2} + 1357 x_{1} + 12 \neq 0\), \(49 x_{1} - 29 \neq 0\), \(147 x_{1}^{2} - 76 x_{1} - 11 \neq 0\), \(3 \neq 0\), \(98 x_{1}^{2} - 67 x_{1} + 3 \neq 0\), \(2401 x_{1}^{3} - 2744 x_{1}^{2} + 633 x_{1} + 86 \neq 0\), \(2401 x_{1}^{3} - 2548 x_{1}^{2} + 541 x_{1} + 78 \neq 0\), \(21609 x_{1}^{4} - 21315 x_{1}^{3} + 2745 x_{1}^{2} + 1187 x_{1} + 78 \neq 0\), \(2401 x_{1}^{4} - 5341 x_{1}^{3} + 3399 x_{1}^{2} - 387 x_{1} - 152 \neq 0\), \(1372 x_{1}^{3} - 2261 x_{1}^{2} + 1090 x_{1} - 129 \neq 0\), \(1372 x_{1}^{3} - 2261 x_{1}^{2} + 1062 x_{1} - 117 \neq 0\), \(2401 x_{1}^{4} - 6713 x_{1}^{3} + 5905 x_{1}^{2} - 1835 x_{1} + 114 \neq 0\), \(1715 x_{1}^{3} - 4823 x_{1}^{2} + 4085 x_{1} - 1089 \neq 0\), \(1715 x_{1}^{3} - 4627 x_{1}^{2} + 3685 x_{1} - 917 \neq 0\), \(21609 x_{1}^{4} - 55958 x_{1}^{3} + 41644 x_{1}^{2} - 7482 x_{1} - 1221 \neq 0\), \(3087 x_{1}^{3} - 4144 x_{1}^{2} + 1287 x_{1} + 66 \neq 0\), \(3087 x_{1}^{3} - 4144 x_{1}^{2} + 1259 x_{1} + 78 \neq 0\), \(196 x_{1}^{2} - 183 x_{1} + 35 \neq 0\), \(441 x_{1}^{2} - 277 x_{1} - 4 \neq 0\), \(2401 x_{1}^{3} - 2646 x_{1}^{2} + 741 x_{1} - 8 \neq 0\), \(21609 x_{1}^{4} - 21315 x_{1}^{3} + 2647 x_{1}^{2} + 1387 x_{1} - 8 \neq 0\), \(4802 x_{1}^{4} - 5537 x_{1}^{3} + 1443 x_{1}^{2} + 151 x_{1} - 43 \neq 0\), \(9604 x_{1}^{4} - 25823 x_{1}^{3} + 24117 x_{1}^{2} - 9589 x_{1} + 1419 \neq 0\), \(9604 x_{1}^{4} - 25823 x_{1}^{3} + 23921 x_{1}^{2} - 9245 x_{1} + 1271 \neq 0\), \(21609 x_{1}^{4} - 51499 x_{1}^{3} + 38375 x_{1}^{2} - 9337 x_{1} + 132 \neq 0\), \(21609 x_{1}^{4} - 51499 x_{1}^{3} + 38179 x_{1}^{2} - 8993 x_{1} - 16 \neq 0\), \(9604 x_{1}^{4} - 13475 x_{1}^{3} + 5728 x_{1}^{2} - 531 x_{1} - 86 \neq 0\), \(9604 x_{1}^{4} - 13475 x_{1}^{3} + 5532 x_{1}^{2} - 439 x_{1} - 78 \neq 0\), \(12005 x_{1}^{4} - 16415 x_{1}^{3} + 6383 x_{1}^{2} - 285 x_{1} - 152 \neq 0\), \(2401 x_{1}^{4} - 2940 x_{1}^{3} + 655 x_{1}^{2} + 246 x_{1} - 66 \neq 0\), \(2401 x_{1}^{4} - 2940 x_{1}^{3} + 851 x_{1}^{2} + 154 x_{1} - 74 \neq 0\), \(12005 x_{1}^{4} - 13328 x_{1}^{3} + 3072 x_{1}^{2} + 400 x_{1} - 37 \neq 0\), \(21609 x_{1}^{4} - 23716 x_{1}^{3} + 5489 x_{1}^{2} + 554 x_{1} - 8 \neq 0\), \(9604 x_{1}^{4} - 25823 x_{1}^{3} + 23921 x_{1}^{2} - 9245 x_{1} + 1287 \neq 0\), \(21609 x_{1}^{4} - 51499 x_{1}^{3} + 37983 x_{1}^{2} - 8649 x_{1} - 148 \neq 0\) |
| Realization matrix | \(\begin{pmatrix}1 & 0 & 1 & 4 & 4 & 4 & 0 & 4 & 0 & 4 & 2 & 4 \\ 0 & 1 & 1 & 245 x_{1} - 153 & -21 x_{1} + 17 & 49 x_{1} - 29 & 2 & -49 x_{1} + 33 & 0 & -49 x_{1} + 33 & 0 & -21 x_{1} + 17 \\ 0 & 0 & 0 & 4 & 28 x_{1} - 16 & 4 & 35 x_{1} - 19 & 28 x_{1} - 16 & 1 & -14 x_{1} + 10 & -7 x_{1} + 5 & 4 x_{1}\end{pmatrix}\) |
Combinatorics
Computed on the fly from the id.
Bases (204)
{1,2,4} {1,3,4} {2,3,4} {1,2,5} {1,3,5} {2,3,5} {2,4,5} {3,4,5} {1,2,6} {1,3,6} {2,3,6} {1,4,6} {3,4,6} {1,5,6} {2,5,6} {4,5,6} {1,2,7} {1,3,7} {2,3,7} {1,4,7} {2,4,7} {1,5,7} {2,5,7} {3,5,7} {4,5,7} {1,6,7} {2,6,7} {3,6,7} {4,6,7} {5,6,7} {1,2,8} {1,3,8} {2,3,8} {1,4,8} {2,4,8} {3,4,8} {1,5,8} {3,5,8} {4,5,8} {1,6,8} {2,6,8} {3,6,8} {4,6,8} {5,6,8} {2,7,8} {3,7,8} {4,7,8} {5,7,8} {6,7,8} {1,2,9} {1,3,9} {2,3,9} {1,4,9} {2,4,9} {3,4,9} {1,5,9} {2,5,9} {3,5,9} {4,5,9} {1,6,9} {2,6,9} {3,6,9} {4,6,9} {5,6,9} {1,7,9} {3,7,9} {4,7,9} {5,7,9} {6,7,9} {1,8,9} {2,8,9} {3,8,9} {4,8,9} {5,8,9} {6,8,9} {7,8,9} {1,2,10} {1,3,10} {2,3,10} {1,4,10} {2,4,10} {3,4,10} {1,5,10} {2,5,10} {3,5,10} {4,5,10} {1,6,10} {2,6,10} {3,6,10} {4,6,10} {5,6,10} {1,7,10} {2,7,10} {3,7,10} {4,7,10} {5,7,10} {1,8,10} {2,8,10} {3,8,10} {4,8,10} {5,8,10} {6,8,10} {7,8,10} {1,9,10} {2,9,10} {3,9,10} {4,9,10} {5,9,10} {6,9,10} {7,9,10} {1,2,11} {1,3,11} {2,3,11} {1,4,11} {2,4,11} {3,4,11} {1,5,11} {2,5,11} {3,5,11} {4,5,11} {1,6,11} {2,6,11} {3,6,11} {4,6,11} {5,6,11} {1,7,11} {2,7,11} {3,7,11} {4,7,11} {5,7,11} {6,7,11} {1,8,11} {2,8,11} {3,8,11} {4,8,11} {5,8,11} {7,8,11} {2,9,11} {3,9,11} {4,9,11} {5,9,11} {6,9,11} {7,9,11} {8,9,11} {1,10,11} {3,10,11} {4,10,11} {5,10,11} {6,10,11} {7,10,11} {8,10,11} {9,10,11} {1,2,12} {1,3,12} {2,3,12} {1,4,12} {2,4,12} {3,4,12} {1,5,12} {2,5,12} {3,5,12} {4,5,12} {1,6,12} {2,6,12} {3,6,12} {4,6,12} {5,6,12} {1,7,12} {2,7,12} {3,7,12} {4,7,12} {5,7,12} {6,7,12} {1,8,12} {2,8,12} {3,8,12} {4,8,12} {5,8,12} {6,8,12} {7,8,12} {1,9,12} {2,9,12} {3,9,12} {4,9,12} {6,9,12} {7,9,12} {8,9,12} {2,10,12} {3,10,12} {4,10,12} {5,10,12} {6,10,12} {7,10,12} {8,10,12} {9,10,12} {1,11,12} {2,11,12} {3,11,12} {5,11,12} {6,11,12} {7,11,12} {8,11,12} {9,11,12} {10,11,12}Non-bases (16)
{1,2,3} {1,4,5} {2,4,6} {3,5,6} {3,4,7} {2,5,8} {1,7,8} {2,7,9} {6,7,10} {8,9,10} {6,8,11} {1,9,11} {2,10,11} {5,9,12} {1,10,12} {4,11,12}Circuits (367)
{1,2,3} {1,4,5} {2,3,4,5} {2,4,6} {1,3,4,6} {1,2,5,6} {3,5,6} {1,2,4,7} {3,4,7} {1,2,5,7} {1,3,5,7} {2,3,5,7} {2,4,5,7} {1,2,6,7} {1,3,6,7} {2,3,6,7} {1,4,6,7} {1,5,6,7} {2,5,6,7} {4,5,6,7} {1,2,4,8} {1,3,4,8} {2,3,4,8} {2,5,8} {1,3,5,8} {3,4,5,8} {1,2,6,8} {1,3,6,8} {2,3,6,8} {1,4,6,8} {3,4,6,8} {1,5,6,8} {4,5,6,8} {1,7,8} {2,3,7,8} {2,4,7,8} {3,5,7,8} {4,5,7,8} {2,6,7,8} {3,6,7,8} {4,6,7,8} {5,6,7,8} {1,2,4,9} {1,3,4,9} {2,3,4,9} {1,2,5,9} {1,3,5,9} {2,3,5,9} {2,4,5,9} {3,4,5,9} {1,2,6,9} {1,3,6,9} {2,3,6,9} {1,4,6,9} {3,4,6,9} {1,5,6,9} {2,5,6,9} {4,5,6,9} {2,7,9} {1,3,7,9} {1,4,7,9} {1,5,7,9} {3,5,7,9} {4,5,7,9} {1,6,7,9} {3,6,7,9} {4,6,7,9} {5,6,7,9} {1,2,8,9} {1,3,8,9} {2,3,8,9} {1,4,8,9} {2,4,8,9} {3,4,8,9} {1,5,8,9} {3,5,8,9} {4,5,8,9} {1,6,8,9} {2,6,8,9} {3,6,8,9} {4,6,8,9} {5,6,8,9} {3,7,8,9} {4,7,8,9} {5,7,8,9} {6,7,8,9} {1,2,4,10} {1,3,4,10} {2,3,4,10} {1,2,5,10} {1,3,5,10} {2,3,5,10} {2,4,5,10} {3,4,5,10} {1,2,6,10} {1,3,6,10} {2,3,6,10} {1,4,6,10} {3,4,6,10} {1,5,6,10} {2,5,6,10} {4,5,6,10} {1,2,7,10} {1,3,7,10} {2,3,7,10} {1,4,7,10} {2,4,7,10} {1,5,7,10} {2,5,7,10} {3,5,7,10} {4,5,7,10} {6,7,10} {1,2,8,10} {1,3,8,10} {2,3,8,10} {1,4,8,10} {2,4,8,10} {3,4,8,10} {1,5,8,10} {3,5,8,10} {4,5,8,10} {1,6,8,10} {2,6,8,10} {3,6,8,10} {4,6,8,10} {5,6,8,10} {2,7,8,10} {3,7,8,10} {4,7,8,10} {5,7,8,10} {1,2,9,10} {1,3,9,10} {2,3,9,10} {1,4,9,10} {2,4,9,10} {3,4,9,10} {1,5,9,10} {2,5,9,10} {3,5,9,10} {4,5,9,10} {1,6,9,10} {2,6,9,10} {3,6,9,10} {4,6,9,10} {5,6,9,10} {1,7,9,10} {3,7,9,10} {4,7,9,10} {5,7,9,10} {8,9,10} {1,2,4,11} {1,3,4,11} {2,3,4,11} {1,2,5,11} {1,3,5,11} {2,3,5,11} {2,4,5,11} {3,4,5,11} {1,2,6,11} {1,3,6,11} {2,3,6,11} {1,4,6,11} {3,4,6,11} {1,5,6,11} {2,5,6,11} {4,5,6,11} {1,2,7,11} {1,3,7,11} {2,3,7,11} {1,4,7,11} {2,4,7,11} {1,5,7,11} {2,5,7,11} {3,5,7,11} {4,5,7,11} {1,6,7,11} {2,6,7,11} {3,6,7,11} {4,6,7,11} {5,6,7,11} {1,2,8,11} {1,3,8,11} {2,3,8,11} {1,4,8,11} {2,4,8,11} {3,4,8,11} {1,5,8,11} {3,5,8,11} {4,5,8,11} {6,8,11} {2,7,8,11} {3,7,8,11} {4,7,8,11} {5,7,8,11} {1,9,11} {2,3,9,11} {2,4,9,11} {3,4,9,11} {2,5,9,11} {3,5,9,11} {4,5,9,11} {2,6,9,11} {3,6,9,11} {4,6,9,11} {5,6,9,11} {3,7,9,11} {4,7,9,11} {5,7,9,11} {6,7,9,11} {2,8,9,11} {3,8,9,11} {4,8,9,11} {5,8,9,11} {7,8,9,11} {2,10,11} {1,3,10,11} {1,4,10,11} {3,4,10,11} {1,5,10,11} {3,5,10,11} {4,5,10,11} {1,6,10,11} {3,6,10,11} {4,6,10,11} {5,6,10,11} {1,7,10,11} {3,7,10,11} {4,7,10,11} {5,7,10,11} {1,8,10,11} {3,8,10,11} {4,8,10,11} {5,8,10,11} {7,8,10,11} {3,9,10,11} {4,9,10,11} {5,9,10,11} {6,9,10,11} {7,9,10,11} {1,2,4,12} {1,3,4,12} {2,3,4,12} {1,2,5,12} {1,3,5,12} {2,3,5,12} {2,4,5,12} {3,4,5,12} {1,2,6,12} {1,3,6,12} {2,3,6,12} {1,4,6,12} {3,4,6,12} {1,5,6,12} {2,5,6,12} {4,5,6,12} {1,2,7,12} {1,3,7,12} {2,3,7,12} {1,4,7,12} {2,4,7,12} {1,5,7,12} {2,5,7,12} {3,5,7,12} {4,5,7,12} {1,6,7,12} {2,6,7,12} {3,6,7,12} {4,6,7,12} {5,6,7,12} {1,2,8,12} {1,3,8,12} {2,3,8,12} {1,4,8,12} {2,4,8,12} {3,4,8,12} {1,5,8,12} {3,5,8,12} {4,5,8,12} {1,6,8,12} {2,6,8,12} {3,6,8,12} {4,6,8,12} {5,6,8,12} {2,7,8,12} {3,7,8,12} {4,7,8,12} {5,7,8,12} {6,7,8,12} {1,2,9,12} {1,3,9,12} {2,3,9,12} {1,4,9,12} {2,4,9,12} {3,4,9,12} {5,9,12} {1,6,9,12} {2,6,9,12} {3,6,9,12} {4,6,9,12} {1,7,9,12} {3,7,9,12} {4,7,9,12} {6,7,9,12} {1,8,9,12} {2,8,9,12} {3,8,9,12} {4,8,9,12} {6,8,9,12} {7,8,9,12} {1,10,12} {2,3,10,12} {2,4,10,12} {3,4,10,12} {2,5,10,12} {3,5,10,12} {4,5,10,12} {2,6,10,12} {3,6,10,12} {4,6,10,12} {5,6,10,12} {2,7,10,12} {3,7,10,12} {4,7,10,12} {5,7,10,12} {2,8,10,12} {3,8,10,12} {4,8,10,12} {5,8,10,12} {6,8,10,12} {7,8,10,12} {2,9,10,12} {3,9,10,12} {4,9,10,12} {6,9,10,12} {7,9,10,12} {1,2,11,12} {1,3,11,12} {2,3,11,12} {4,11,12} {1,5,11,12} {2,5,11,12} {3,5,11,12} {1,6,11,12} {2,6,11,12} {3,6,11,12} {5,6,11,12} {1,7,11,12} {2,7,11,12} {3,7,11,12} {5,7,11,12} {6,7,11,12} {1,8,11,12} {2,8,11,12} {3,8,11,12} {5,8,11,12} {7,8,11,12} {2,9,11,12} {3,9,11,12} {6,9,11,12} {7,9,11,12} {8,9,11,12} {3,10,11,12} {5,10,11,12} {6,10,11,12} {7,10,11,12} {8,10,11,12} {9,10,11,12}Flats by rank (48)
- rank 0 (1): {}
- rank 1 (12): {1} {2} {3} {4} {5} {6} {7} {8} {9} {10} {11} {12}
- rank 2 (34): {1,2,3} {1,4,5} {1,6} {2,4,6} {3,5,6} {3,4,7} {5,7} {3,8} {4,8} {2,5,8} {1,7,8} {3,9} {4,9} {6,9} {2,7,9} {3,10} {4,10} {5,10} {6,7,10} {8,9,10} {3,11} {5,11} {7,11} {6,8,11} {1,9,11} {2,10,11} {2,12} {3,12} {6,12} {7,12} {8,12} {5,9,12} {1,10,12} {4,11,12}
- rank 3 (1): {1,2,3,4,5,6,7,8,9,10,11,12}
Hyperplanes (34)
{1,2,3} {1,4,5} {1,6} {2,4,6} {3,5,6} {3,4,7} {5,7} {3,8} {4,8} {2,5,8} {1,7,8} {3,9} {4,9} {6,9} {2,7,9} {3,10} {4,10} {5,10} {6,7,10} {8,9,10} {3,11} {5,11} {7,11} {6,8,11} {1,9,11} {2,10,11} {2,12} {3,12} {6,12} {7,12} {8,12} {5,9,12} {1,10,12} {4,11,12}Lines (16)
{1,2,3} {1,4,5} {2,4,6} {3,5,6} {3,4,7} {2,5,8} {1,7,8} {2,7,9} {6,7,10} {8,9,10} {6,8,11} {1,9,11} {2,10,11} {5,9,12} {1,10,12} {4,11,12}Dual (rank 9)
Revlex encoding in this labeling (not canonicalized, so not linked): ******0***********0***0***************************************0********0*0**************************0**************0*******************************0*********************0*******0****************0******0***0******0******0
Bases: {3,5,6,7,8,9,10,11,12} {2,5,6,7,8,9,10,11,12} {1,5,6,7,8,9,10,11,12} {3,4,6,7,8,9,10,11,12} {2,4,6,7,8,9,10,11,12} {1,4,6,7,8,9,10,11,12} {1,3,6,7,8,9,10,11,12} {1,2,6,7,8,9,10,11,12} {3,4,5,7,8,9,10,11,12} {2,4,5,7,8,9,10,11,12} {1,4,5,7,8,9,10,11,12} {2,3,5,7,8,9,10,11,12} {1,2,5,7,8,9,10,11,12} {2,3,4,7,8,9,10,11,12} {1,3,4,7,8,9,10,11,12} {1,2,3,7,8,9,10,11,12} {3,4,5,6,8,9,10,11,12} {2,4,5,6,8,9,10,11,12} {1,4,5,6,8,9,10,11,12} {2,3,5,6,8,9,10,11,12} {1,3,5,6,8,9,10,11,12} {2,3,4,6,8,9,10,11,12} {1,3,4,6,8,9,10,11,12} {1,2,4,6,8,9,10,11,12} {1,2,3,6,8,9,10,11,12} {2,3,4,5,8,9,10,11,12} {1,3,4,5,8,9,10,11,12} {1,2,4,5,8,9,10,11,12} {1,2,3,5,8,9,10,11,12} {1,2,3,4,8,9,10,11,12} {3,4,5,6,7,9,10,11,12} {2,4,5,6,7,9,10,11,12} {1,4,5,6,7,9,10,11,12} {2,3,5,6,7,9,10,11,12} {1,3,5,6,7,9,10,11,12} {1,2,5,6,7,9,10,11,12} {2,3,4,6,7,9,10,11,12} {1,2,4,6,7,9,10,11,12} {1,2,3,6,7,9,10,11,12} {2,3,4,5,7,9,10,11,12} {1,3,4,5,7,9,10,11,12} {1,2,4,5,7,9,10,11,12} {1,2,3,5,7,9,10,11,12} {1,2,3,4,7,9,10,11,12} {1,3,4,5,6,9,10,11,12} {1,2,4,5,6,9,10,11,12} {1,2,3,5,6,9,10,11,12} {1,2,3,4,6,9,10,11,12} {1,2,3,4,5,9,10,11,12} {3,4,5,6,7,8,10,11,12} {2,4,5,6,7,8,10,11,12} {1,4,5,6,7,8,10,11,12} {2,3,5,6,7,8,10,11,12} {1,3,5,6,7,8,10,11,12} {1,2,5,6,7,8,10,11,12} {2,3,4,6,7,8,10,11,12} {1,3,4,6,7,8,10,11,12} {1,2,4,6,7,8,10,11,12} {1,2,3,6,7,8,10,11,12} {2,3,4,5,7,8,10,11,12} {1,3,4,5,7,8,10,11,12} {1,2,4,5,7,8,10,11,12} {1,2,3,5,7,8,10,11,12} {1,2,3,4,7,8,10,11,12} {2,3,4,5,6,8,10,11,12} {1,2,4,5,6,8,10,11,12} {1,2,3,5,6,8,10,11,12} {1,2,3,4,6,8,10,11,12} {1,2,3,4,5,8,10,11,12} {2,3,4,5,6,7,10,11,12} {1,3,4,5,6,7,10,11,12} {1,2,4,5,6,7,10,11,12} {1,2,3,5,6,7,10,11,12} {1,2,3,4,6,7,10,11,12} {1,2,3,4,5,7,10,11,12} {1,2,3,4,5,6,10,11,12} {3,4,5,6,7,8,9,11,12} {2,4,5,6,7,8,9,11,12} {1,4,5,6,7,8,9,11,12} {2,3,5,6,7,8,9,11,12} {1,3,5,6,7,8,9,11,12} {1,2,5,6,7,8,9,11,12} {2,3,4,6,7,8,9,11,12} {1,3,4,6,7,8,9,11,12} {1,2,4,6,7,8,9,11,12} {1,2,3,6,7,8,9,11,12} {2,3,4,5,7,8,9,11,12} {1,3,4,5,7,8,9,11,12} {1,2,4,5,7,8,9,11,12} {1,2,3,5,7,8,9,11,12} {1,2,3,4,7,8,9,11,12} {2,3,4,5,6,8,9,11,12} {1,3,4,5,6,8,9,11,12} {1,2,4,5,6,8,9,11,12} {1,2,3,5,6,8,9,11,12} {1,2,3,4,6,8,9,11,12} {2,3,4,5,6,7,9,11,12} {1,3,4,5,6,7,9,11,12} {1,2,4,5,6,7,9,11,12} {1,2,3,5,6,7,9,11,12} {1,2,3,4,6,7,9,11,12} {1,2,3,4,5,7,9,11,12} {1,2,3,4,5,6,9,11,12} {2,3,4,5,6,7,8,11,12} {1,3,4,5,6,7,8,11,12} {1,2,4,5,6,7,8,11,12} {1,2,3,5,6,7,8,11,12} {1,2,3,4,6,7,8,11,12} {1,2,3,4,5,7,8,11,12} {1,2,3,4,5,6,8,11,12} {3,4,5,6,7,8,9,10,12} {2,4,5,6,7,8,9,10,12} {1,4,5,6,7,8,9,10,12} {2,3,5,6,7,8,9,10,12} {1,3,5,6,7,8,9,10,12} {1,2,5,6,7,8,9,10,12} {2,3,4,6,7,8,9,10,12} {1,3,4,6,7,8,9,10,12} {1,2,4,6,7,8,9,10,12} {1,2,3,6,7,8,9,10,12} {2,3,4,5,7,8,9,10,12} {1,3,4,5,7,8,9,10,12} {1,2,4,5,7,8,9,10,12} {1,2,3,5,7,8,9,10,12} {1,2,3,4,7,8,9,10,12} {2,3,4,5,6,8,9,10,12} {1,3,4,5,6,8,9,10,12} {1,2,4,5,6,8,9,10,12} {1,2,3,5,6,8,9,10,12} {1,2,3,4,6,8,9,10,12} {1,2,3,4,5,8,9,10,12} {2,3,4,5,6,7,9,10,12} {1,3,4,5,6,7,9,10,12} {1,2,4,5,6,7,9,10,12} {1,2,3,5,6,7,9,10,12} {1,2,3,4,6,7,9,10,12} {1,2,3,4,5,6,9,10,12} {1,3,4,5,6,7,8,10,12} {1,2,4,5,6,7,8,10,12} {1,2,3,5,6,7,8,10,12} {1,2,3,4,6,7,8,10,12} {1,2,3,4,5,7,8,10,12} {1,2,3,4,5,6,8,10,12} {1,2,3,4,5,6,7,10,12} {2,3,4,5,6,7,8,9,12} {1,2,4,5,6,7,8,9,12} {1,2,3,5,6,7,8,9,12} {1,2,3,4,6,7,8,9,12} {1,2,3,4,5,7,8,9,12} {1,2,3,4,5,6,8,9,12} {1,2,3,4,5,6,7,9,12} {1,2,3,4,5,6,7,8,12} {3,4,5,6,7,8,9,10,11} {2,4,5,6,7,8,9,10,11} {1,4,5,6,7,8,9,10,11} {2,3,5,6,7,8,9,10,11} {1,3,5,6,7,8,9,10,11} {1,2,5,6,7,8,9,10,11} {2,3,4,6,7,8,9,10,11} {1,3,4,6,7,8,9,10,11} {1,2,4,6,7,8,9,10,11} {1,2,3,6,7,8,9,10,11} {2,3,4,5,7,8,9,10,11} {1,3,4,5,7,8,9,10,11} {1,2,4,5,7,8,9,10,11} {1,2,3,5,7,8,9,10,11} {1,2,3,4,7,8,9,10,11} {2,3,4,5,6,8,9,10,11} {1,3,4,5,6,8,9,10,11} {1,2,4,5,6,8,9,10,11} {1,2,3,5,6,8,9,10,11} {1,2,3,4,6,8,9,10,11} {1,2,3,4,5,8,9,10,11} {2,3,4,5,6,7,9,10,11} {1,3,4,5,6,7,9,10,11} {1,2,4,5,6,7,9,10,11} {1,2,3,5,6,7,9,10,11} {1,2,3,4,6,7,9,10,11} {1,2,3,4,5,7,9,10,11} {1,2,3,4,5,6,9,10,11} {2,3,4,5,6,7,8,10,11} {1,3,4,5,6,7,8,10,11} {1,2,4,5,6,7,8,10,11} {1,2,3,5,6,7,8,10,11} {1,2,3,4,5,7,8,10,11} {1,2,3,4,5,6,8,10,11} {1,2,3,4,5,6,7,10,11} {1,3,4,5,6,7,8,9,11} {1,2,4,5,6,7,8,9,11} {1,2,3,5,6,7,8,9,11} {1,2,3,4,6,7,8,9,11} {1,2,3,4,5,7,8,9,11} {1,2,3,4,5,6,8,9,11} {1,2,3,4,5,6,7,9,11} {1,2,3,4,5,6,7,8,11} {2,3,4,5,6,7,8,9,10} {1,3,4,5,6,7,8,9,10} {1,2,4,5,6,7,8,9,10} {1,2,3,4,6,7,8,9,10} {1,2,3,4,5,7,8,9,10} {1,2,3,4,5,6,8,9,10} {1,2,3,4,5,6,7,9,10} {1,2,3,4,5,6,7,8,10} {1,2,3,4,5,6,7,8,9}
Loops: none. Parallel classes of size > 1: none.
Downloads
- Record as JSON
- OSCAR:
matroid_from_revlex_basis_encoding("0******0******0***0******0****************0*******0*********************0*******************************0**************0**************************0*0********0***************************************0***0***********0******", 3, 12)