Matroid 3.12.26520960

Label	3.12.26520960
Id	`r3_n12_0000**********0*****000***00*0******00**********************0******************00**********0*********************00*******************0************************0*****0`
Rank	3
n	12

Affine diagram.

Basic invariants

Bases	198
Circuits	328
Flats	45
Cyclic flats	15
Loops	0
Connected components	1
Automorphisms	1
Beta invariant	26
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	8
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	1,3,5

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: `37`
Realization space: is regular scheme	not computed
Realization space: singular fiber primes	not computed
Realization space: singular fiber characteristics	p = 37 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

\(T = x_{0}^{3} + 9 x_{0}^{2} + 3 x_{0} x_{1}^{2} + 16 x_{0} x_{1} + 26 x_{0} + x_{1}^{9} + 3 x_{1}^{8} + 6 x_{1}^{7} + 10 x_{1}^{6} + 15 x_{1}^{5} + 21 x_{1}^{4} + 28 x_{1}^{3} + 33 x_{1}^{2} + 26 x_{1}\)

Realization space

Ring	\(\mathbb{Z}[x_{1}]\)
Defining ideal	\(\left(5 x_{1}^{3} - 14 x_{1}^{2} + 10 x_{1} - 2\right)\)
Inequations	\(25 x_{1}^{5} - 205 x_{1}^{4} + 563 x_{1}^{3} - 633 x_{1}^{2} + 264 x_{1} - 36 \neq 0\), \(25 x_{1}^{5} - 205 x_{1}^{4} + 568 x_{1}^{3} - 662 x_{1}^{2} + 308 x_{1} - 48 \neq 0\), \(5 x_{1}^{2} - 19 x_{1} + 6 \neq 0\), \(x_{1} - 2 \neq 0\), \(5 x_{1}^{3} - 29 x_{1}^{2} + 42 x_{1} - 12 \neq 0\), \(5 x_{1}^{3} - 19 x_{1}^{2} + 23 x_{1} - 6 \neq 0\), \(25 x_{1}^{5} - 205 x_{1}^{4} + 573 x_{1}^{3} - 671 x_{1}^{2} + 310 x_{1} - 48 \neq 0\), \(x_{1} \neq 0\), \(5 x_{1}^{2} - 9 x_{1} + 2 \neq 0\), \(5 x_{1}^{3} - 19 x_{1}^{2} + 22 x_{1} - 6 \neq 0\), \(10 x_{1}^{3} - 28 x_{1}^{2} + 25 x_{1} - 6 \neq 0\), \(25 x_{1}^{5} - 120 x_{1}^{4} + 215 x_{1}^{3} - 180 x_{1}^{2} + 74 x_{1} - 12 \neq 0\), \(25 x_{1}^{6} - 165 x_{1}^{5} + 436 x_{1}^{4} - 576 x_{1}^{3} + 395 x_{1}^{2} - 135 x_{1} + 18 \neq 0\), \(25 x_{1}^{5} - 120 x_{1}^{4} + 215 x_{1}^{3} - 180 x_{1}^{2} + 73 x_{1} - 12 \neq 0\), \(5 x_{1}^{2} - 11 x_{1} + 4 \neq 0\), \(2 \neq 0\), \(5 x_{1}^{2} - 10 x_{1} + 4 \neq 0\), \(5 x_{1}^{4} - 29 x_{1}^{3} + 52 x_{1}^{2} - 33 x_{1} + 6 \neq 0\), \(25 x_{1}^{5} - 145 x_{1}^{4} + 330 x_{1}^{3} - 356 x_{1}^{2} + 174 x_{1} - 30 \neq 0\), \(5 x_{1}^{3} - 19 x_{1}^{2} + 24 x_{1} - 6 \neq 0\), \(25 x_{1}^{5} - 145 x_{1}^{4} + 330 x_{1}^{3} - 346 x_{1}^{2} + 154 x_{1} - 24 \neq 0\), \(5 x_{1}^{4} - 29 x_{1}^{3} + 62 x_{1}^{2} - 52 x_{1} + 12 \neq 0\), \(5 x_{1}^{3} - 19 x_{1}^{2} + 24 x_{1} - 8 \neq 0\), \(50 x_{1}^{6} - 380 x_{1}^{5} + 1117 x_{1}^{4} - 1611 x_{1}^{3} + 1192 x_{1}^{2} - 430 x_{1} + 60 \neq 0\), \(50 x_{1}^{6} - 380 x_{1}^{5} + 1117 x_{1}^{4} - 1601 x_{1}^{3} + 1164 x_{1}^{2} - 406 x_{1} + 54 \neq 0\), \(50 x_{1}^{5} - 330 x_{1}^{4} + 787 x_{1}^{3} - 824 x_{1}^{2} + 368 x_{1} - 60 \neq 0\), \(5 x_{1}^{2} - 14 x_{1} + 10 \neq 0\), \(15 x_{1}^{3} - 77 x_{1}^{2} + 108 x_{1} - 30 \neq 0\), \(5 x_{1}^{3} - 29 x_{1}^{2} + 42 x_{1} - 10 \neq 0\), \(5 x_{1}^{2} - 14 x_{1} + 6 \neq 0\), \(5 x_{1}^{3} - 4 x_{1}^{2} - 8 x_{1} + 6 \neq 0\), \(5 x_{1}^{4} - 9 x_{1}^{3} - 4 x_{1}^{2} + 16 x_{1} - 6 \neq 0\), \(50 x_{1}^{6} - 380 x_{1}^{5} + 1117 x_{1}^{4} - 1591 x_{1}^{3} + 1146 x_{1}^{2} - 402 x_{1} + 54 \neq 0\)
Realization matrix	\(\begin{pmatrix}1 & 1 & 0 & 1 & 0 & 1 & 2 & 1 & 0 & 0 & 2 & 1 \\ 0 & 1 & 1 & -10 x_{1}^{2} + 23 x_{1} - 7 & 0 & 0 & 0 & 1 & 1 & x_{1} & -20 x_{1}^{2} + 46 x_{1} - 14 & -5 x_{1}^{2} + 10 x_{1} - 3 \\ 0 & 0 & 0 & 0 & 1 & 1 & -5 x_{1}^{2} + 14 x_{1} - 4 & 1 & -1 & x_{1} - 1 & 15 x_{1}^{2} - 32 x_{1} + 10 & x_{1}\end{pmatrix}\)

Combinatorics

Computed on the fly from the id.

Bases (198)

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

Non-bases (22)

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

Circuits (328)

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

Flats by rank (45)

rank 0 (1): {}
rank 1 (12): {1} {2} {3} {4} {5} {6} {7} {8} {9} {10} {11} {12}
rank 2 (31): {1,2,3,4} {2,7} {3,7} {1,5,6,7} {1,8} {2,5,8} {3,6,8} {4,7,8} {1,9} {4,9} {2,6,9} {8,9} {2,10} {4,10} {6,10} {8,10} {3,5,9,10} {2,11} {3,11} {4,5,11} {6,11} {7,9,11} {1,10,11} {1,12} {2,12} {3,12} {5,12} {4,6,12} {9,12} {7,10,12} {8,11,12}
rank 3 (1): {1,2,3,4,5,6,7,8,9,10,11,12}

Hyperplanes (31)

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

Lines (13)

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

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***0*********0************0000

Bases: {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} {2,3,6,7,8,9,10,11,12} {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} {1,3,5,7,8,9,10,11,12} {1,2,5,7,8,9,10,11,12} {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} {1,2,5,6,8,9,10,11,12} {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} {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} {1,2,3,4,6,9,10,11,12} {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} {1,2,4,5,7,8,10,11,12} {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} {1,2,3,6,7,8,9,11,12} {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} {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} {1,2,3,5,6,7,8,11,12} {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} {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} {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} {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} {1,2,3,4,7,8,9,10,11} {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} {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} {1,2,4,5,6,7,8,9,11} {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} {1,2,3,4,5,6,7,9,11} {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} {1,2,3,4,6,7,8,9,10} {1,2,3,4,5,7,8,9,10} {1,2,3,4,5,6,8,9,10} {1,2,3,4,5,6,7,8,10} {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("0000************0*********0***0***0*******0****0*****0**********0**0************************0*********************0*0************0************************0*0*********************0****************************0*********0**", 3, 12)