Matroid 3.12.3350340

Label	3.12.3350340
Id	`r3_n12_0****0**00***0************0************************0************************0***********0**********************0*****0*0***************************00******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 over ℚ	1
Components of realization space over ℚ̄	3
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	2,3,6

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	no how determined: smoothness method: `univariate_resultant_and_localized_gcd` smoothness witness: `23`
Realization space: is regular scheme	not computed
Realization space: singular fiber primes	not computed
Realization space: singular fiber characteristics	p = 23 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

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	\(\left(5 x_{1}^{3} - 7 x_{1}^{2} - 5 x_{1} - 1\right)\)
Inequations	\(5 x_{1}^{2} - 10 x_{1} + 1 \neq 0\), \(5 x_{1}^{2} - 2 x_{1} + 1 \neq 0\), \(5 x_{1}^{2} - 8 x_{1} - 1 \neq 0\), \(25 x_{1}^{4} - 60 x_{1}^{3} - 10 x_{1}^{2} + 44 x_{1} + 33 \neq 0\), \(5 x_{1}^{2} - 6 x_{1} - 7 \neq 0\), \(5 x_{1}^{2} - 7 x_{1} - 4 \neq 0\), \(175 x_{1}^{4} - 560 x_{1}^{3} + 326 x_{1}^{2} + 176 x_{1} + 43 \neq 0\), \(x_{1} - 1 \neq 0\), \(5 x_{1}^{2} - 8 x_{1} - 5 \neq 0\), \(5 x_{1}^{2} - 6 x_{1} - 3 \neq 0\), \(5 x_{1} + 3 \neq 0\), \(x_{1} + 1 \neq 0\), \(5 x_{1} - 7 \neq 0\), \(2 \neq 0\), \(175 x_{1}^{4} - 490 x_{1}^{3} + 128 x_{1}^{2} + 282 x_{1} + 65 \neq 0\), \(5 x_{1}^{2} - 12 x_{1} - 5 \neq 0\), \(5 x_{1}^{2} - 12 x_{1} - 1 \neq 0\), \(35 x_{1}^{2} - 64 x_{1} - 11 \neq 0\), \(30 x_{1}^{3} - 47 x_{1}^{2} - 18 x_{1} - 5 \neq 0\), \(10 x_{1}^{2} - 19 x_{1} - 1 \neq 0\), \(3 x_{1} + 1 \neq 0\), \(15 x_{1}^{2} - 26 x_{1} - 5 \neq 0\), \(5 \neq 0\), \(7 x_{1}^{2} - 12 x_{1} - 3 \neq 0\), \(25 x_{1}^{4} - 80 x_{1}^{3} + 38 x_{1}^{2} + 44 x_{1} + 5 \neq 0\), \(5 x_{1} + 1 \neq 0\), \(5 x_{1}^{3} - 17 x_{1}^{2} + 13 x_{1} + 3 \neq 0\), \(50 x_{1}^{4} - 165 x_{1}^{3} + 103 x_{1}^{2} + 53 x_{1} + 7 \neq 0\), \(15 x_{1}^{2} - 26 x_{1} - 13 \neq 0\), \(15 x_{1}^{2} - 26 x_{1} - 9 \neq 0\), \(45 x_{1}^{2} - 78 x_{1} - 19 \neq 0\), \(5 x_{1}^{2} - 12 x_{1} + 3 \neq 0\), \(75 x_{1}^{4} - 310 x_{1}^{3} + 252 x_{1}^{2} + 114 x_{1} + 29 \neq 0\), \(75 x_{1}^{4} - 310 x_{1}^{3} + 242 x_{1}^{2} + 138 x_{1} + 23 \neq 0\), \(20 x_{1}^{2} - 33 x_{1} - 11 \neq 0\), \(5 x_{1}^{2} - 8 x_{1} - 3 \neq 0\), \(10 x_{1}^{2} - 17 x_{1} - 5 \neq 0\), \(25 x_{1}^{4} - 100 x_{1}^{3} + 66 x_{1}^{2} + 60 x_{1} + 5 \neq 0\), \(25 x_{1}^{4} - 100 x_{1}^{3} + 86 x_{1}^{2} + 28 x_{1} - 7 \neq 0\), \(25 x_{1}^{2} - 50 x_{1} + 1 \neq 0\), \(2 x_{1}^{2} - 3 x_{1} - 1 \neq 0\), \(15 x_{1}^{3} - 21 x_{1}^{2} - 13 x_{1} - 5 \neq 0\), \(x_{1}^{2} - 2 x_{1} - 1 \neq 0\), \(5 x_{1}^{2} - 10 x_{1} - 3 \neq 0\), \(25 x_{1}^{4} - 100 x_{1}^{3} + 96 x_{1}^{2} + 16 x_{1} - 13 \neq 0\), \(25 x_{1}^{4} - 130 x_{1}^{3} + 178 x_{1}^{2} - 26 x_{1} - 23 \neq 0\), \(75 x_{1}^{4} - 280 x_{1}^{3} + 160 x_{1}^{2} + 180 x_{1} + 33 \neq 0\), \(75 x_{1}^{4} - 310 x_{1}^{3} + 272 x_{1}^{2} + 86 x_{1} + 13 \neq 0\), \(15 x_{1}^{2} - 26 x_{1} - 7 \neq 0\), \(15 x_{1}^{2} - 26 x_{1} - 3 \neq 0\)
Realization matrix	\(\begin{pmatrix}1 & 1 & 0 & 1 & 0 & 0 & 2 & 4 & 4 & 2 & 4 & 4 \\ 1 & 0 & 1 & 0 & 1 & 0 & -15 x_{1}^{2} + 26 x_{1} + 5 & 5 x_{1}^{2} - 12 x_{1} - 1 & 15 x_{1}^{2} - 26 x_{1} - 9 & 5 x_{1}^{2} - 10 x_{1} - 3 & 15 x_{1}^{2} - 26 x_{1} - 9 & 5 x_{1}^{2} - 12 x_{1} - 1 \\ 0 & 0 & 0 & 1 & -1 & 1 & 2 & -5 x_{1}^{2} + 12 x_{1} + 1 & -5 x_{1}^{2} + 10 x_{1} + 3 & 2 x_{1} & -5 x_{1}^{2} + 12 x_{1} + 1 & 4 x_{1}\end{pmatrix}\)

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