Matroid 3.12.3967941

Label	3.12.3967941
Id	`r3_n12_0****0**00***0************0************************0***0****************0***0***************************0*******0*0****************************0*************00*******`
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	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	1,3,9

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	\(\left(12 x_{1}^{2} - 20 x_{1} + 9\right)\)
Inequations	\(6 x_{1}^{2} - 8 x_{1} + 3 \neq 0\), \(6 x_{1}^{4} + 17 x_{1}^{3} - 52 x_{1}^{2} + 40 x_{1} - 9 \neq 0\), \(6 x_{1}^{2} - 11 x_{1} + 6 \neq 0\), \(36 x_{1}^{4} - 120 x_{1}^{3} + 157 x_{1}^{2} - 96 x_{1} + 24 \neq 0\), \(216 x_{1}^{6} - 936 x_{1}^{5} + 1734 x_{1}^{4} - 1740 x_{1}^{3} + 989 x_{1}^{2} - 298 x_{1} + 36 \neq 0\), \(3 \neq 0\), \(12 x_{1}^{4} + 2 x_{1}^{3} - 39 x_{1}^{2} + 36 x_{1} - 9 \neq 0\), \(36 x_{1}^{4} - 102 x_{1}^{3} + 112 x_{1}^{2} - 57 x_{1} + 12 \neq 0\), \(216 x_{1}^{5} - 720 x_{1}^{4} + 978 x_{1}^{3} - 660 x_{1}^{2} + 217 x_{1} - 27 \neq 0\), \(36 x_{1}^{4} - 102 x_{1}^{3} + 112 x_{1}^{2} - 54 x_{1} + 9 \neq 0\), \(432 x_{1}^{8} - 1152 x_{1}^{7} - 264 x_{1}^{6} + 4850 x_{1}^{5} - 8363 x_{1}^{4} + 7072 x_{1}^{3} - 3302 x_{1}^{2} + 810 x_{1} - 81 \neq 0\), \(1296 x_{1}^{8} - 7344 x_{1}^{7} + 18540 x_{1}^{6} - 27120 x_{1}^{5} + 25050 x_{1}^{4} - 14903 x_{1}^{3} + 5550 x_{1}^{2} - 1176 x_{1} + 108 \neq 0\), \(3 x_{1}^{3} + 7 x_{1}^{2} - 18 x_{1} + 9 \neq 0\), \(3 x_{1} - 1 \neq 0\), \(2 x_{1} - 3 \neq 0\), \(36 x_{1}^{4} - 120 x_{1}^{3} + 139 x_{1}^{2} - 69 x_{1} + 12 \neq 0\), \(36 x_{1}^{4} - 120 x_{1}^{3} + 157 x_{1}^{2} - 93 x_{1} + 21 \neq 0\), \(36 x_{1}^{5} - 138 x_{1}^{4} + 106 x_{1}^{3} + 60 x_{1}^{2} - 96 x_{1} + 27 \neq 0\), \(36 x_{1}^{4} - 120 x_{1}^{3} + 159 x_{1}^{2} - 95 x_{1} + 21 \neq 0\), \(36 x_{1}^{5} - 138 x_{1}^{4} + 108 x_{1}^{3} + 58 x_{1}^{2} - 96 x_{1} + 27 \neq 0\), \(6 x_{1}^{4} + 17 x_{1}^{3} - 51 x_{1}^{2} + 39 x_{1} - 9 \neq 0\), \(x_{1} \neq 0\), \(36 x_{1}^{4} - 108 x_{1}^{3} + 123 x_{1}^{2} - 62 x_{1} + 12 \neq 0\), \(18 x_{1}^{4} - 48 x_{1}^{3} + 32 x_{1}^{2} + 6 x_{1} - 9 \neq 0\), \(1296 x_{1}^{8} - 7560 x_{1}^{7} + 19476 x_{1}^{6} - 28818 x_{1}^{5} + 26694 x_{1}^{4} - 15797 x_{1}^{3} + 5811 x_{1}^{2} - 1209 x_{1} + 108 \neq 0\), \(1296 x_{1}^{9} - 7776 x_{1}^{8} + 19692 x_{1}^{7} - 26856 x_{1}^{6} + 20206 x_{1}^{5} - 6557 x_{1}^{4} - 1505 x_{1}^{3} + 2120 x_{1}^{2} - 702 x_{1} + 81 \neq 0\), \(72 x_{1}^{4} - 204 x_{1}^{3} + 230 x_{1}^{2} - 119 x_{1} + 24 \neq 0\), \(36 x_{1}^{4} - 120 x_{1}^{3} + 151 x_{1}^{2} - 84 x_{1} + 18 \neq 0\), \(216 x_{1}^{7} - 1080 x_{1}^{6} + 2130 x_{1}^{5} - 2006 x_{1}^{4} + 722 x_{1}^{3} + 206 x_{1}^{2} - 243 x_{1} + 54 \neq 0\), \(36 x_{1}^{6} + 48 x_{1}^{5} - 441 x_{1}^{4} + 750 x_{1}^{3} - 566 x_{1}^{2} + 201 x_{1} - 27 \neq 0\), \(216 x_{1}^{6} - 936 x_{1}^{5} + 1734 x_{1}^{4} - 1746 x_{1}^{3} + 1003 x_{1}^{2} - 309 x_{1} + 39 \neq 0\), \(1296 x_{1}^{8} - 7344 x_{1}^{7} + 18540 x_{1}^{6} - 27120 x_{1}^{5} + 25044 x_{1}^{4} - 14889 x_{1}^{3} + 5539 x_{1}^{2} - 1173 x_{1} + 108 \neq 0\), \(324 x_{1}^{6} - 1512 x_{1}^{5} + 3024 x_{1}^{4} - 3309 x_{1}^{3} + 2089 x_{1}^{2} - 723 x_{1} + 108 \neq 0\), \(36 x_{1}^{3} - 72 x_{1}^{2} + 53 x_{1} - 12 \neq 0\), \(216 x_{1}^{6} - 972 x_{1}^{5} + 1818 x_{1}^{4} - 1815 x_{1}^{3} + 1019 x_{1}^{2} - 303 x_{1} + 36 \neq 0\), \(108 x_{1}^{6} - 450 x_{1}^{5} + 702 x_{1}^{4} - 436 x_{1}^{3} - 30 x_{1}^{2} + 159 x_{1} - 54 \neq 0\), \(36 x_{1}^{4} - 108 x_{1}^{3} + 119 x_{1}^{2} - 57 x_{1} + 9 \neq 0\), \(216 x_{1}^{7} - 1008 x_{1}^{6} + 1866 x_{1}^{5} - 1604 x_{1}^{4} + 402 x_{1}^{3} + 340 x_{1}^{2} - 267 x_{1} + 54 \neq 0\), \(36 x_{1}^{6} + 12 x_{1}^{5} - 345 x_{1}^{4} + 645 x_{1}^{3} - 511 x_{1}^{2} + 189 x_{1} - 27 \neq 0\), \(36 x_{1}^{3} - 72 x_{1}^{2} + 49 x_{1} - 12 \neq 0\), \(36 x_{1}^{4} - 108 x_{1}^{3} + 121 x_{1}^{2} - 60 x_{1} + 12 \neq 0\), \(18 x_{1}^{4} - 30 x_{1}^{3} + 10 x_{1}^{2} + 6 x_{1} - 3 \neq 0\), \(6 x_{1}^{4} + 11 x_{1}^{3} - 42 x_{1}^{2} + 36 x_{1} - 9 \neq 0\), \(1296 x_{1}^{7} - 6264 x_{1}^{6} + 13212 x_{1}^{5} - 15642 x_{1}^{4} + 11148 x_{1}^{3} - 4744 x_{1}^{2} + 1105 x_{1} - 108 \neq 0\), \(648 x_{1}^{6} - 2808 x_{1}^{5} + 5166 x_{1}^{4} - 5136 x_{1}^{3} + 2894 x_{1}^{2} - 871 x_{1} + 108 \neq 0\), \(648 x_{1}^{6} - 2484 x_{1}^{5} + 4086 x_{1}^{4} - 3633 x_{1}^{3} + 1829 x_{1}^{2} - 489 x_{1} + 54 \neq 0\), \(324 x_{1}^{6} - 1566 x_{1}^{5} + 3204 x_{1}^{4} - 3540 x_{1}^{3} + 2224 x_{1}^{2} - 753 x_{1} + 108 \neq 0\), \(648 x_{1}^{8} - 3564 x_{1}^{7} + 8028 x_{1}^{6} - 9276 x_{1}^{5} + 5248 x_{1}^{4} - 480 x_{1}^{3} - 1064 x_{1}^{2} + 540 x_{1} - 81 \neq 0\), \(648 x_{1}^{7} - 3132 x_{1}^{6} + 6606 x_{1}^{5} - 7821 x_{1}^{4} + 5574 x_{1}^{3} - 2372 x_{1}^{2} + 552 x_{1} - 54 \neq 0\), \(1296 x_{1}^{9} - 7776 x_{1}^{8} + 19692 x_{1}^{7} - 26856 x_{1}^{6} + 20200 x_{1}^{5} - 6540 x_{1}^{4} - 1522 x_{1}^{3} + 2126 x_{1}^{2} - 702 x_{1} + 81 \neq 0\), \(216 x_{1}^{8} - 216 x_{1}^{7} - 1998 x_{1}^{6} + 6590 x_{1}^{5} - 9352 x_{1}^{4} + 7370 x_{1}^{3} - 3338 x_{1}^{2} + 810 x_{1} - 81 \neq 0\), \(108 x_{1}^{7} - 54 x_{1}^{6} - 1008 x_{1}^{5} + 2740 x_{1}^{4} - 3250 x_{1}^{3} + 2033 x_{1}^{2} - 648 x_{1} + 81 \neq 0\), \(48 x_{1}^{5} - 104 x_{1}^{4} + 2 x_{1}^{3} + 140 x_{1}^{2} - 114 x_{1} + 27 \neq 0\), \(48 x_{1}^{5} - 104 x_{1}^{4} + 6 x_{1}^{3} + 136 x_{1}^{2} - 114 x_{1} + 27 \neq 0\)
Realization matrix	\(\begin{pmatrix}1 & 1 & 0 & x_{1}^{2} & x_{1} & x_{1} & 1 & 0 & 0 & 1 & x_{1} & 1 \\ 0 & 1 & 1 & -6 x_{1}^{4} - 11 x_{1}^{3} + 7 x_{1}^{2} + 24 x_{1} - 18 & -4 x_{1}^{2} + 7 x_{1} - 3 & -2 x_{1}^{2} + 5 x_{1} - 3 & 0 & x_{1} - 1 & 0 & 6 x_{1}^{2} - 9 x_{1} + 4 & -4 x_{1}^{2} + 7 x_{1} - 3 & 6 x_{1}^{2} - 9 x_{1} + 4 \\ 0 & 0 & 0 & x_{1}^{2} & -2 x_{1}^{2} + 3 x_{1} & -2 x_{1}^{2} + 3 x_{1} & 1 & 6 x_{1}^{3} - x_{1}^{2} - 13 x_{1} + 9 & 1 & -6 x_{1}^{2} + 9 x_{1} - 3 & -6 x_{1}^{3} + 9 x_{1}^{2} - 3 x_{1} & x_{1}\end{pmatrix}\)

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

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

Dual (rank 9)

Revlex encoding in this labeling (not canonicalized, so not linked): *********00*****************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} {1,2,3,5,6,7,10,11,12} {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} {1,2,4,5,6,7,8,11,12} {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} {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} {1,2,3,4,5,7,8,10,12} {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} {1,2,3,5,6,7,8,9,12} {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} {1,2,3,4,5,6,8,10,11} {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} {1,2,3,4,5,6,8,9,11} {1,2,3,4,5,6,7,9,11} {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*****************00*********", 3, 12)