Matroid 3.12.2083738

Label	3.12.2083738
Id	`r3_n12_0****0**0******0****0***00**************0****************************0*********0***********************0********00*************************0*********0***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	2,3,4

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	no how determined: smoothness method: `univariate_resultant_and_localized_gcd` smoothness witness: `11`
Realization space: is regular scheme	not computed
Realization space: singular fiber primes	not computed
Realization space: singular fiber characteristics	p = 11 how determined: singular fiber characteristics method: `reused_univariate_resultant_and_localized_gcd`
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	\(\left(x_{1}^{3} - 7 x_{1}^{2} + 5 x_{1} - 1\right)\)
Inequations	\(2 x_{1}^{3} - 14 x_{1}^{2} + 11 x_{1} - 3 \neq 0\), \(x_{1}^{6} - 19 x_{1}^{5} + 128 x_{1}^{4} - 341 x_{1}^{3} + 255 x_{1}^{2} - 70 x_{1} + 6 \neq 0\), \(x_{1}^{2} - 6 x_{1} + 3 \neq 0\), \(x_{1} - 1 \neq 0\), \(x_{1}^{6} - 21 x_{1}^{5} + 155 x_{1}^{4} - 448 x_{1}^{3} + 360 x_{1}^{2} - 113 x_{1} + 12 \neq 0\), \(x_{1}^{4} - 14 x_{1}^{3} + 55 x_{1}^{2} - 41 x_{1} + 9 \neq 0\), \(x_{1}^{6} - 21 x_{1}^{5} + 157 x_{1}^{4} - 475 x_{1}^{3} + 463 x_{1}^{2} - 185 x_{1} + 27 \neq 0\), \(2 \neq 0\), \(x_{1}^{2} - 7 x_{1} + 2 \neq 0\), \(x_{1}^{4} - 14 x_{1}^{3} + 55 x_{1}^{2} - 41 x_{1} + 8 \neq 0\), \(2 x_{1}^{3} - 13 x_{1}^{2} + 4 x_{1} - 1 \neq 0\), \(x_{1}^{6} - 20 x_{1}^{5} + 142 x_{1}^{4} - 400 x_{1}^{3} + 328 x_{1}^{2} - 107 x_{1} + 12 \neq 0\), \(x_{1}^{6} - 20 x_{1}^{5} + 142 x_{1}^{4} - 400 x_{1}^{3} + 329 x_{1}^{2} - 112 x_{1} + 14 \neq 0\), \(x_{1}^{6} - 20 x_{1}^{5} + 141 x_{1}^{4} - 387 x_{1}^{3} + 282 x_{1}^{2} - 81 x_{1} + 8 \neq 0\), \(x_{1}^{6} - 20 x_{1}^{5} + 141 x_{1}^{4} - 388 x_{1}^{3} + 289 x_{1}^{2} - 83 x_{1} + 8 \neq 0\), \(x_{1}^{4} - 16 x_{1}^{3} + 67 x_{1}^{2} - 39 x_{1} + 7 \neq 0\), \(2 x_{1}^{5} - 29 x_{1}^{4} + 129 x_{1}^{3} - 175 x_{1}^{2} + 82 x_{1} - 13 \neq 0\), \(2 x_{1}^{5} - 28 x_{1}^{4} + 115 x_{1}^{3} - 121 x_{1}^{2} + 47 x_{1} - 7 \neq 0\), \(2 x_{1}^{7} - 39 x_{1}^{6} + 268 x_{1}^{5} - 725 x_{1}^{4} + 554 x_{1}^{3} - 131 x_{1}^{2} - 12 x_{1} + 6 \neq 0\), \(2 x_{1}^{7} - 40 x_{1}^{6} + 287 x_{1}^{5} - 854 x_{1}^{4} + 920 x_{1}^{3} - 518 x_{1}^{2} + 151 x_{1} - 18 \neq 0\), \(2 x_{1}^{7} - 41 x_{1}^{6} + 307 x_{1}^{5} - 995 x_{1}^{4} + 1313 x_{1}^{3} - 837 x_{1}^{2} + 255 x_{1} - 30 \neq 0\), \(2 x_{1}^{3} - 13 x_{1}^{2} + 5 x_{1} - 1 \neq 0\), \(2 x_{1}^{6} - 41 x_{1}^{5} + 296 x_{1}^{4} - 847 x_{1}^{3} + 726 x_{1}^{2} - 248 x_{1} + 30 \neq 0\), \(2 x_{1}^{4} - 27 x_{1}^{3} + 102 x_{1}^{2} - 66 x_{1} + 13 \neq 0\), \(x_{1}^{4} - 13 x_{1}^{3} + 47 x_{1}^{2} - 25 x_{1} + 4 \neq 0\), \(x_{1}^{6} - 21 x_{1}^{5} + 157 x_{1}^{4} - 481 x_{1}^{3} + 508 x_{1}^{2} - 211 x_{1} + 31 \neq 0\), \(x_{1}^{6} - 21 x_{1}^{5} + 156 x_{1}^{4} - 467 x_{1}^{3} + 455 x_{1}^{2} - 183 x_{1} + 27 \neq 0\), \(x_{1}^{6} - 21 x_{1}^{5} + 156 x_{1}^{4} - 467 x_{1}^{3} + 454 x_{1}^{2} - 176 x_{1} + 25 \neq 0\), \(x_{1}^{4} - 14 x_{1}^{3} + 54 x_{1}^{2} - 34 x_{1} + 7 \neq 0\), \(x_{1}^{4} - 13 x_{1}^{3} + 48 x_{1}^{2} - 32 x_{1} + 7 \neq 0\), \(x_{1}^{4} - 13 x_{1}^{3} + 48 x_{1}^{2} - 32 x_{1} + 6 \neq 0\)
Realization matrix	\(\begin{pmatrix}1 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 1 & 1 & 1 & 1 \\ 1 & 0 & 1 & 0 & 1 & 0 & 1 & -x_{1}^{2} + 7 x_{1} - 2 & 2 x_{1} & -x_{1}^{2} + 6 x_{1} - 1 & -x_{1}^{2} + 6 x_{1} - 1 & -x_{1}^{2} + 7 x_{1} - 2 \\ 0 & 0 & 0 & 1 & 1 & -x_{1}^{2} + 7 x_{1} - 2 & x_{1}^{2} - 7 x_{1} + 3 & -x_{1}^{2} + 7 x_{1} - 2 & -x_{1}^{2} + x_{1} & x_{1} & -x_{1} + 1 & x_{1}\end{pmatrix}\)

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

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

Hyperplanes (34)

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

Lines (16)

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

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