Matroid 3.12.1976068

Label	3.12.1976068
Id	`r3_n12_0****0**0******0****0***0*****************0***********0*********0**************0*****************0***0*******************************************0***00*******0***`
Rank	3
n	12

Affine diagram.

Basic invariants

Bases	204
Circuits	367
Flats	48
Cyclic flats	18
Loops	0
Connected components	1
Automorphisms	1
Beta invariant	29
Girth	3
Simple	yes
Connected	yes
Uniform	not computed
Loopless	yes
Coloopless	yes
Paving	yes
Laminar	no
Nested	no
Self dual	no
Identically self dual	no
Series parallel	no
Transversal	no
Supersolvable	no
Divisionally free	no
Orientable	yes
Three lines	yes

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

Status	computed_realization_space
Dimension of realization space	7
Expected dimension over ℤ	1
Components of realization space	not computed
Free realization space	no
Principal ideal	yes
Birational type	not computed
Birational type components	not computed
Good basis	not computed
Good basis v2	3,5,6

Geometry

Realization space: scheme simple core id	not computed
Smooth char 0	not computed
Singular primes	not computed
Realization space: smooth over ℚ	yes
Realization space: smooth over ℤ	yes how determined: smoothness method: `univariate_resultant_and_localized_gcd` smoothness witness: `—`
Realization space: is regular scheme	not computed
Realization space: singular fiber primes	not computed
Realization space: singular fiber characteristics	none how determined: singular fiber characteristics method: `smooth_over_ZZ`
Realization space: characteristic dimensions	show [ { "p": 0, "d": 0 } ] how determined: characteristic dimensions method: `primitive_hypersurface_flat`
Realization space: characteristic dimension unexpected	no
Realization space: characteristic dimension varies	no

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	\(\left(2 x_{1}^{3} - 3 x_{1}^{2} + 4 x_{1} - 1\right)\)
Inequations	\(x_{1} - 1 \neq 0\), \(2 x_{1}^{2} - 3 x_{1} + 3 \neq 0\), \(16 x_{1}^{3} - 30 x_{1}^{2} + 39 x_{1} - 17 \neq 0\), \(4 x_{1}^{2} - 5 x_{1} + 6 \neq 0\), \(x_{1}^{2} - 2 x_{1} + 2 \neq 0\), \(16 x_{1}^{6} - 56 x_{1}^{5} + 118 x_{1}^{4} - 143 x_{1}^{3} + 113 x_{1}^{2} - 46 x_{1} + 8 \neq 0\), \(16 x_{1}^{6} - 52 x_{1}^{5} + 100 x_{1}^{4} - 101 x_{1}^{3} + 57 x_{1}^{2} - 2 x_{1} - 8 \neq 0\), \(32 x_{1}^{5} - 124 x_{1}^{4} + 254 x_{1}^{3} - 296 x_{1}^{2} + 207 x_{1} - 62 \neq 0\), \(16 x_{1}^{5} - 52 x_{1}^{4} + 84 x_{1}^{3} - 73 x_{1}^{2} + 27 x_{1} + 2 \neq 0\), \(2 x_{1}^{3} - 7 x_{1}^{2} + 8 x_{1} - 5 \neq 0\), \(4 x_{1}^{5} - 16 x_{1}^{4} + 31 x_{1}^{3} - 30 x_{1}^{2} + 17 x_{1} - 2 \neq 0\), \(2 x_{1}^{2} - x_{1} + 1 \neq 0\), \(16 x_{1}^{5} - 62 x_{1}^{4} + 131 x_{1}^{3} - 155 x_{1}^{2} + 113 x_{1} - 35 \neq 0\), \(32 x_{1}^{6} - 108 x_{1}^{5} + 216 x_{1}^{4} - 243 x_{1}^{3} + 173 x_{1}^{2} - 56 x_{1} + 2 \neq 0\), \(2 \neq 0\), \(32 x_{1}^{6} - 108 x_{1}^{5} + 216 x_{1}^{4} - 241 x_{1}^{3} + 168 x_{1}^{2} - 49 x_{1} - 2 \neq 0\), \(2 x_{1}^{4} - 5 x_{1}^{3} + 9 x_{1}^{2} - 6 x_{1} + 2 \neq 0\), \(2 x_{1}^{3} - 5 x_{1}^{2} + 7 x_{1} - 2 \neq 0\), \(40 x_{1}^{6} - 152 x_{1}^{5} + 328 x_{1}^{4} - 423 x_{1}^{3} + 351 x_{1}^{2} - 166 x_{1} + 32 \neq 0\), \(48 x_{1}^{6} - 188 x_{1}^{5} + 412 x_{1}^{4} - 539 x_{1}^{3} + 449 x_{1}^{2} - 212 x_{1} + 40 \neq 0\), \(48 x_{1}^{6} - 188 x_{1}^{5} + 396 x_{1}^{4} - 503 x_{1}^{3} + 399 x_{1}^{2} - 184 x_{1} + 36 \neq 0\), \(2 x_{1}^{4} - 11 x_{1}^{3} + 18 x_{1}^{2} - 17 x_{1} + 6 \neq 0\), \(6 x_{1}^{5} - 25 x_{1}^{4} + 54 x_{1}^{3} - 63 x_{1}^{2} + 44 x_{1} - 12 \neq 0\), \(6 x_{1}^{3} - 11 x_{1}^{2} + 13 x_{1} - 6 \neq 0\), \(6 x_{1}^{2} - 7 x_{1} + 6 \neq 0\), \(96 x_{1}^{6} - 388 x_{1}^{5} + 832 x_{1}^{4} - 1095 x_{1}^{3} + 908 x_{1}^{2} - 453 x_{1} + 102 \neq 0\), \(12 x_{1}^{5} - 44 x_{1}^{4} + 85 x_{1}^{3} - 89 x_{1}^{2} + 56 x_{1} - 12 \neq 0\), \(96 x_{1}^{6} - 388 x_{1}^{5} + 864 x_{1}^{4} - 1157 x_{1}^{3} + 991 x_{1}^{2} - 494 x_{1} + 104 \neq 0\), \(96 x_{1}^{6} - 388 x_{1}^{5} + 864 x_{1}^{4} - 1155 x_{1}^{3} + 986 x_{1}^{2} - 487 x_{1} + 100 \neq 0\), \(3 x_{1} - 2 \neq 0\), \(2 x_{1}^{4} - x_{1}^{3} - x_{1}^{2} + 6 x_{1} - 4 \neq 0\), \(2 x_{1}^{3} - 5 x_{1}^{2} + 5 x_{1} - 4 \neq 0\), \(32 x_{1}^{6} - 140 x_{1}^{5} + 308 x_{1}^{4} - 435 x_{1}^{3} + 386 x_{1}^{2} - 222 x_{1} + 62 \neq 0\), \(12 x_{1}^{6} - 32 x_{1}^{5} + 39 x_{1}^{4} - 11 x_{1}^{3} - 28 x_{1}^{2} + 32 x_{1} - 8 \neq 0\), \(8 x_{1}^{5} - 30 x_{1}^{4} + 57 x_{1}^{3} - 63 x_{1}^{2} + 38 x_{1} - 8 \neq 0\), \(12 x_{1}^{6} - 32 x_{1}^{5} + 51 x_{1}^{4} - 29 x_{1}^{3} - 8 x_{1}^{2} + 32 x_{1} - 16 \neq 0\), \(32 x_{1}^{5} - 124 x_{1}^{4} + 256 x_{1}^{3} - 301 x_{1}^{2} + 212 x_{1} - 64 \neq 0\), \(32 x_{1}^{6} - 140 x_{1}^{5} + 340 x_{1}^{4} - 497 x_{1}^{3} + 469 x_{1}^{2} - 263 x_{1} + 64 \neq 0\), \(16 x_{1}^{6} - 68 x_{1}^{5} + 164 x_{1}^{4} - 221 x_{1}^{3} + 191 x_{1}^{2} - 80 x_{1} + 8 \neq 0\), \(4 x_{1}^{6} - 20 x_{1}^{5} + 49 x_{1}^{4} - 76 x_{1}^{3} + 71 x_{1}^{2} - 40 x_{1} + 8 \neq 0\), \(32 x_{1}^{6} - 108 x_{1}^{5} + 184 x_{1}^{4} - 179 x_{1}^{3} + 85 x_{1}^{2} - 10 x_{1} - 2 \neq 0\), \(32 x_{1}^{6} - 140 x_{1}^{5} + 308 x_{1}^{4} - 443 x_{1}^{3} + 400 x_{1}^{2} - 241 x_{1} + 70 \neq 0\), \(32 x_{1}^{4} - 62 x_{1}^{3} + 83 x_{1}^{2} - 41 x_{1} + 2 \neq 0\), \(32 x_{1}^{5} - 124 x_{1}^{4} + 264 x_{1}^{3} - 315 x_{1}^{2} + 231 x_{1} - 72 \neq 0\), \(32 x_{1}^{5} - 124 x_{1}^{4} + 232 x_{1}^{3} - 255 x_{1}^{2} + 153 x_{1} - 36 \neq 0\), \(32 x_{1}^{6} - 108 x_{1}^{5} + 216 x_{1}^{4} - 239 x_{1}^{3} + 163 x_{1}^{2} - 44 x_{1} - 4 \neq 0\), \(4 x_{1}^{6} - 20 x_{1}^{5} + 53 x_{1}^{4} - 78 x_{1}^{3} + 73 x_{1}^{2} - 36 x_{1} + 8 \neq 0\)
Realization matrix	\(\begin{pmatrix}1 & 2 & 1 & 2 & 0 & 0 & 0 & 2 & 2 & 2 & 1 & 1 \\ 1 & -2 x_{1}^{2} + 3 x_{1} - 1 & 0 & -2 x_{1}^{2} + 3 x_{1} - 1 & 1 & 0 & 1 & -2 x_{1}^{2} + 4 x_{1} - 2 & -2 x_{1}^{2} + x_{1} - 1 & 2 & x_{1}^{2} + 1 & -x_{1}^{2} + 2 x_{1} - 1 \\ 1 & -2 x_{1}^{2} + 3 x_{1} - 1 & 0 & 2 & 0 & 1 & -6 x_{1}^{2} + 7 x_{1} - 9 & -2 x_{1}^{2} + 3 x_{1} - 1 & 0 & -2 x_{1}^{2} + 3 x_{1} - 2 & x_{1} & x_{1}\end{pmatrix}\)

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} {3,5,6} {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} {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} {1,7,8} {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} {4,5,9} {1,6,9} {2,6,9} {3,6,9} {4,6,9} {5,6,9} {1,7,9} {2,7,9} {3,7,9} {4,7,9} {5,7,9} {6,7,9} {1,8,9} {2,8,9} {3,8,9} {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} {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} {6,7,10} {1,8,10} {2,8,10} {3,8,10} {4,8,10} {5,8,10} {6,8,10} {7,8,10} {1,9,10} {3,9,10} {4,9,10} {5,9,10} {6,9,10} {7,9,10} {8,9,10} {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} {2,7,11} {3,7,11} {4,7,11} {5,7,11} {6,7,11} {1,8,11} {2,8,11} {4,8,11} {5,8,11} {6,8,11} {7,8,11} {1,9,11} {2,9,11} {3,9,11} {4,9,11} {5,9,11} {6,9,11} {7,9,11} {8,9,11} {1,10,11} {2,10,11} {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} {7,8,12} {1,9,12} {2,9,12} {3,9,12} {4,9,12} {5,9,12} {6,9,12} {8,9,12} {1,10,12} {2,10,12} {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} {4,11,12} {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} {3,4,7} {5,6,7} {2,5,8} {3,5,9} {4,8,9} {1,6,10} {2,9,10} {1,7,11} {3,8,11} {6,8,12} {7,9,12} {3,10,12} {5,11,12}

Circuits (367)

{1,2,3} {1,4,5} {2,3,4,5} {2,4,6} {1,3,4,6} {1,2,5,6} {1,3,5,6} {2,3,5,6} {3,4,5,6} {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} {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} {3,5,6,8} {4,5,6,8} {1,2,7,8} {1,3,7,8} {2,3,7,8} {1,4,7,8} {2,4,7,8} {1,5,7,8} {3,5,7,8} {4,5,7,8} {1,6,7,8} {2,6,7,8} {3,6,7,8} {4,6,7,8} {1,2,4,9} {1,3,4,9} {2,3,4,9} {1,2,5,9} {3,5,9} {2,4,5,9} {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} {1,2,7,9} {1,3,7,9} {2,3,7,9} {1,4,7,9} {2,4,7,9} {1,5,7,9} {2,5,7,9} {4,5,7,9} {1,6,7,9} {2,6,7,9} {3,6,7,9} {4,6,7,9} {1,2,8,9} {1,3,8,9} {2,3,8,9} {4,8,9} {1,5,8,9} {1,6,8,9} {2,6,8,9} {3,6,8,9} {5,6,8,9} {1,7,8,9} {2,7,8,9} {3,7,8,9} {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} {1,6,10} {2,3,6,10} {3,4,6,10} {2,5,6,10} {3,5,6,10} {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} {2,6,7,10} {3,6,7,10} {4,6,7,10} {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} {2,6,8,10} {3,6,8,10} {4,6,8,10} {5,6,8,10} {1,7,8,10} {2,7,8,10} {3,7,8,10} {4,7,8,10} {5,7,8,10} {6,7,8,10} {2,9,10} {1,3,9,10} {1,4,9,10} {3,4,9,10} {1,5,9,10} {4,5,9,10} {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} {6,7,9,10} {1,8,9,10} {3,8,9,10} {5,8,9,10} {6,8,9,10} {7,8,9,10} {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} {3,5,6,11} {4,5,6,11} {1,7,11} {2,3,7,11} {2,4,7,11} {2,5,7,11} {3,5,7,11} {4,5,7,11} {2,6,7,11} {3,6,7,11} {4,6,7,11} {1,2,8,11} {3,8,11} {1,4,8,11} {2,4,8,11} {1,5,8,11} {4,5,8,11} {1,6,8,11} {2,6,8,11} {4,6,8,11} {5,6,8,11} {2,7,8,11} {4,7,8,11} {5,7,8,11} {6,7,8,11} {1,2,9,11} {1,3,9,11} {2,3,9,11} {1,4,9,11} {2,4,9,11} {3,4,9,11} {1,5,9,11} {2,5,9,11} {4,5,9,11} {1,6,9,11} {2,6,9,11} {3,6,9,11} {4,6,9,11} {5,6,9,11} {2,7,9,11} {3,7,9,11} {4,7,9,11} {5,7,9,11} {6,7,9,11} {1,8,9,11} {2,8,9,11} {5,8,9,11} {6,8,9,11} {7,8,9,11} {1,2,10,11} {1,3,10,11} {2,3,10,11} {1,4,10,11} {2,4,10,11} {3,4,10,11} {1,5,10,11} {2,5,10,11} {3,5,10,11} {4,5,10,11} {2,6,10,11} {3,6,10,11} {4,6,10,11} {5,6,10,11} {2,7,10,11} {3,7,10,11} {4,7,10,11} {5,7,10,11} {6,7,10,11} {1,8,10,11} {2,8,10,11} {4,8,10,11} {5,8,10,11} {6,8,10,11} {7,8,10,11} {1,9,10,11} {3,9,10,11} {4,9,10,11} {5,9,10,11} {6,9,10,11} {7,9,10,11} {8,9,10,11} {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} {3,5,6,12} {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} {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} {6,8,12} {1,7,8,12} {2,7,8,12} {3,7,8,12} {4,7,8,12} {5,7,8,12} {1,2,9,12} {1,3,9,12} {2,3,9,12} {1,4,9,12} {2,4,9,12} {3,4,9,12} {1,5,9,12} {2,5,9,12} {4,5,9,12} {1,6,9,12} {2,6,9,12} {3,6,9,12} {4,6,9,12} {5,6,9,12} {7,9,12} {1,8,9,12} {2,8,9,12} {3,8,9,12} {5,8,9,12} {1,2,10,12} {3,10,12} {1,4,10,12} {2,4,10,12} {1,5,10,12} {2,5,10,12} {4,5,10,12} {2,6,10,12} {4,6,10,12} {5,6,10,12} {1,7,10,12} {2,7,10,12} {4,7,10,12} {5,7,10,12} {6,7,10,12} {1,8,10,12} {2,8,10,12} {4,8,10,12} {5,8,10,12} {7,8,10,12} {1,9,10,12} {4,9,10,12} {5,9,10,12} {6,9,10,12} {8,9,10,12} {1,2,11,12} {1,3,11,12} {2,3,11,12} {1,4,11,12} {2,4,11,12} {3,4,11,12} {5,11,12} {1,6,11,12} {2,6,11,12} {3,6,11,12} {4,6,11,12} {2,7,11,12} {3,7,11,12} {4,7,11,12} {6,7,11,12} {1,8,11,12} {2,8,11,12} {4,8,11,12} {7,8,11,12} {1,9,11,12} {2,9,11,12} {3,9,11,12} {4,9,11,12} {6,9,11,12} {8,9,11,12} {1,10,11,12} {2,10,11,12} {4,10,11,12} {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} {3,6} {2,4,6} {2,7} {3,4,7} {5,6,7} {1,8} {2,5,8} {7,8} {1,9} {3,5,9} {6,9} {4,8,9} {4,10} {5,10} {1,6,10} {7,10} {8,10} {2,9,10} {2,11} {4,11} {6,11} {1,7,11} {3,8,11} {9,11} {10,11} {1,12} {2,12} {4,12} {6,8,12} {7,9,12} {3,10,12} {5,11,12}
rank 3 (1): {1,2,3,4,5,6,7,8,9,10,11,12}

Hyperplanes (34)

{1,2,3} {1,4,5} {3,6} {2,4,6} {2,7} {3,4,7} {5,6,7} {1,8} {2,5,8} {7,8} {1,9} {3,5,9} {6,9} {4,8,9} {4,10} {5,10} {1,6,10} {7,10} {8,10} {2,9,10} {2,11} {4,11} {6,11} {1,7,11} {3,8,11} {9,11} {10,11} {1,12} {2,12} {4,12} {6,8,12} {7,9,12} {3,10,12} {5,11,12}

Lines (16)

{1,2,3} {1,4,5} {2,4,6} {3,4,7} {5,6,7} {2,5,8} {3,5,9} {4,8,9} {1,6,10} {2,9,10} {1,7,11} {3,8,11} {6,8,12} {7,9,12} {3,10,12} {5,11,12}

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} {1,2,4,7,8,9,10,11,12} {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} {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} {2,3,4,5,6,9,10,11,12} {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} {1,2,3,6,7,8,10,11,12} {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} {1,3,4,5,6,8,10,11,12} {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} {1,2,3,4,6,7,10,11,12} {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} {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} {1,2,3,4,5,8,9,11,12} {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} {1,2,4,5,6,7,8,11,12} {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} {1,2,3,4,5,6,7,11,12} {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} {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} {1,2,3,5,6,7,9,10,12} {1,2,3,4,6,7,9,10,12} {1,2,3,4,5,7,9,10,12} {1,2,3,4,5,6,9,10,12} {2,3,4,5,6,7,8,10,12} {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} {1,3,4,5,6,7,8,9,12} {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} {1,2,3,4,5,6,9,10,11} {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} {1,2,3,4,6,7,8,10,11} {1,2,3,4,5,7,8,10,11} {1,2,3,4,5,6,7,10,11} {2,3,4,5,6,7,8,9,11} {1,3,4,5,6,7,8,9,11} {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} {1,2,3,5,6,7,8,9,10} {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)