Matroid 3.12.3440977

Label	3.12.3440977
Id	`r3_n12_0****0**00***0************0************************0************************0***0*0****************************00******0**********************************000*******`
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 over ℚ	1
Components of realization space over ℚ̄	2
Components of realization space	not computed
Free realization space	no
Principal ideal	yes
Birational type	not computed
Birational type components	not computed
Kodaira dimension	not computed
Kodaira dimension components	not computed
Good basis	not computed
Good basis v2	1,4,10

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

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	\(\left(5 x_{1}^{2} - 6 x_{1} + 2\right)\)
Inequations	\(50 x_{1}^{2} - 75 x_{1} + 32 \neq 0\), \(375 x_{1}^{4} - 1060 x_{1}^{3} + 1137 x_{1}^{2} - 544 x_{1} + 96 \neq 0\), \(5 x_{1} - 4 \neq 0\), \(2 \neq 0\), \(5 x_{1}^{2} - 8 x_{1} + 4 \neq 0\), \(5 \neq 0\), \(20 x_{1}^{2} - 29 x_{1} + 12 \neq 0\), \(5 x_{1}^{3} - 26 x_{1}^{2} + 31 x_{1} - 12 \neq 0\), \(15 x_{1}^{2} - 21 x_{1} + 8 \neq 0\), \(3 x_{1} - 2 \neq 0\), \(x_{1} \neq 0\), \(5 x_{1} - 2 \neq 0\), \(5 x_{1} - 6 \neq 0\), \(5 x_{1}^{2} - 16 x_{1} + 8 \neq 0\), \(90 x_{1}^{3} - 203 x_{1}^{2} + 154 x_{1} - 40 \neq 0\), \(10 x_{1}^{3} + 3 x_{1}^{2} - 9 x_{1} + 4 \neq 0\), \(10 x_{1}^{3} - 2 x_{1}^{2} - 13 x_{1} + 8 \neq 0\), \(75 x_{1}^{4} - 35 x_{1}^{3} - 106 x_{1}^{2} + 106 x_{1} - 24 \neq 0\), \(5 x_{1} + 4 \neq 0\), \(5 x_{1}^{3} - x_{1}^{2} - 9 x_{1} + 8 \neq 0\), \(10 x_{1}^{3} - 32 x_{1}^{2} + 33 x_{1} - 12 \neq 0\), \(60 x_{1}^{3} - 122 x_{1}^{2} + 83 x_{1} - 20 \neq 0\), \(15 x_{1}^{2} - 23 x_{1} + 10 \neq 0\), \(30 x_{1}^{2} - 41 x_{1} + 12 \neq 0\), \(30 x_{1}^{2} - 51 x_{1} + 28 \neq 0\), \(x_{1} - 2 \neq 0\), \(5 x_{1} - 8 \neq 0\), \(15 x_{1}^{3} - 73 x_{1}^{2} + 76 x_{1} - 24 \neq 0\), \(15 x_{1} - 8 \neq 0\), \(3 \neq 0\), \(5 x_{1}^{3} + 29 x_{1}^{2} - 40 x_{1} + 16 \neq 0\), \(5 x_{1}^{3} + 24 x_{1}^{2} - 44 x_{1} + 20 \neq 0\), \(75 x_{1}^{3} - 45 x_{1}^{2} - 54 x_{1} + 44 \neq 0\), \(5 x_{1}^{3} - 26 x_{1}^{2} + 36 x_{1} - 16 \neq 0\), \(30 x_{1}^{3} - 71 x_{1}^{2} + 56 x_{1} - 16 \neq 0\), \(10 x_{1}^{2} - 17 x_{1} + 8 \neq 0\), \(25 x_{1}^{2} - 40 x_{1} + 18 \neq 0\), \(375 x_{1}^{4} - 1135 x_{1}^{3} + 1302 x_{1}^{2} - 668 x_{1} + 128 \neq 0\), \(25 x_{1}^{2} - 36 x_{1} + 16 \neq 0\), \(75 x_{1}^{4} - 55 x_{1}^{3} - 102 x_{1}^{2} + 112 x_{1} - 32 \neq 0\), \(75 x_{1}^{4} - 55 x_{1}^{3} - 92 x_{1}^{2} + 120 x_{1} - 40 \neq 0\), \(75 x_{1}^{4} - 35 x_{1}^{3} - 96 x_{1}^{2} + 104 x_{1} - 32 \neq 0\), \(75 x_{1}^{4} - 45 x_{1}^{3} - 94 x_{1}^{2} + 112 x_{1} - 40 \neq 0\), \(75 x_{1}^{3} - 55 x_{1}^{2} - 32 x_{1} + 28 \neq 0\), \(225 x_{1}^{3} - 455 x_{1}^{2} + 322 x_{1} - 80 \neq 0\), \(225 x_{1}^{4} - 685 x_{1}^{3} + 818 x_{1}^{2} - 454 x_{1} + 100 \neq 0\), \(25 x_{1}^{3} - 70 x_{1}^{2} + 62 x_{1} - 16 \neq 0\), \(25 x_{1}^{3} - 35 x_{1}^{2} + 18 x_{1} - 4 \neq 0\), \(25 x_{1}^{3} - 50 x_{1}^{2} + 37 x_{1} - 10 \neq 0\), \(35 x_{1}^{2} - 42 x_{1} + 16 \neq 0\), \(5 x_{1}^{2} - 11 x_{1} + 8 \neq 0\), \(5 x_{1}^{3} - 31 x_{1}^{2} + 42 x_{1} - 20 \neq 0\), \(5 x_{1}^{3} + 4 x_{1}^{2} - 4 \neq 0\), \(75 x_{1}^{4} - 45 x_{1}^{3} - 104 x_{1}^{2} + 124 x_{1} - 40 \neq 0\), \(5 x_{1}^{3} - x_{1}^{2} - 4 x_{1} + 4 \neq 0\), \(75 x_{1}^{4} - 35 x_{1}^{3} - 106 x_{1}^{2} + 116 x_{1} - 32 \neq 0\), \(5 x_{1}^{2} + 4 x_{1} - 4 \neq 0\), \(15 x_{1}^{3} - 23 x_{1}^{2} + 8 x_{1} + 2 \neq 0\), \(15 x_{1}^{2} - 23 x_{1} + 12 \neq 0\)
Realization matrix	\(\begin{pmatrix}1 & 1 & 2 & 0 & 1 & 1 & 2 & 0 & 2 & 0 & 2 & 4 \\ 0 & 1 & 5 x_{1} - 2 & 1 & 2 x_{1} - 1 & x_{1} & 2 & 2 & 5 x_{1} - 2 & 0 & 2 x_{1} & 8 x_{1} - 4 \\ 0 & 1 & 5 x_{1} - 2 & 0 & 0 & 1 & 5 x_{1} - 2 & 5 x_{1} - 1 & 5 x_{1} - 3 & 1 & 5 x_{1} - 3 & 5 x_{1} - 4\end{pmatrix}\)

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

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

Lines (16)

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

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