Matroid 3.12.3040429

Label	3.12.3040429
Id	`r3_n12_0****0**00***0********************0*****************0***0******************0***00*************************0*******0*********************************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 over ℚ	1
Components of realization space over ℚ̄	4
Components of realization space	not computed
Free realization space	no
Principal ideal	no
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	5,7,9

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	no how determined: smoothness method: `direct_equidimensional_jacobian_certificate` smoothness witness: `257`
Realization space: is regular scheme	not computed
Realization space: singular fiber primes	not computed
Realization space: singular fiber characteristics	p = 257 how determined: singular fiber characteristics method: `reused_direct_equidimensional_jacobian_certificate`
Realization space: characteristic dimensions	show [ { "p": 0, "d": 0 } ] how determined: characteristic dimensions method: `exact_flatness_and_exceptional_fibers`
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	\(\mathbb{Z}[x_{1}, x_{2}]\)
Defining ideal	\(\left(-3 x_{1} + x_{2}^{2} - 3 x_{2} + 4,\ x_{1}^{2} + 2 x_{1} x_{2} + 2 x_{1} + x_{2} - 4\right)\)
Inequations	\(x_{1}^{2} x_{2} + 4 x_{1}^{2} + 4 x_{1} x_{2} - 11 x_{1} - 6 x_{2} + 8 \neq 0\), \(x_{1}^{3} x_{2}^{2} + 4 x_{1}^{3} x_{2} + x_{1}^{3} - 2 x_{1}^{2} x_{2}^{4} - 16 x_{1}^{2} x_{2}^{3} - 21 x_{1}^{2} x_{2}^{2} + 14 x_{1}^{2} x_{2} - 8 x_{1}^{2} - 24 x_{1} x_{2}^{4} - 58 x_{1} x_{2}^{3} + 180 x_{1} x_{2}^{2} - 92 x_{1} x_{2} + 16 x_{1} - 72 x_{2}^{4} + 228 x_{2}^{3} - 224 x_{2}^{2} + 64 x_{2} \neq 0\), \(x_{1} \neq 0\), \(x_{1} x_{2}^{2} + 3 x_{1} x_{2} - 3 x_{1} + 5 x_{2}^{2} - 14 x_{2} + 8 \neq 0\), \(x_{1} x_{2} + 4 x_{1} + 5 x_{2} - 8 \neq 0\), \(x_{1} x_{2} + 4 x_{1} + 6 x_{2} - 8 \neq 0\), \(x_{1} x_{2}^{2} + 4 x_{1} x_{2} + x_{1} + 4 x_{2}^{2} - 7 x_{2} - 1 \neq 0\), \(x_{1}^{2} x_{2} + 4 x_{1}^{2} + 4 x_{1} x_{2} - 12 x_{1} - 6 x_{2} + 8 \neq 0\), \(3 x_{1}^{2} x_{2}^{3} + 12 x_{1}^{2} x_{2}^{2} - 7 x_{1}^{2} x_{2} + x_{1}^{2} + 13 x_{1} x_{2}^{3} - 39 x_{1} x_{2}^{2} + 15 x_{1} x_{2} - x_{1} - 16 x_{2}^{3} + 26 x_{2}^{2} - 8 x_{2} \neq 0\), \(x_{1}^{2} - x_{1} x_{2} - x_{1} + x_{2}^{2} \neq 0\), \(x_{2} \neq 0\), \(x_{1}^{2} x_{2} + 4 x_{1}^{2} - x_{1} x_{2}^{3} - 4 x_{1} x_{2}^{2} + 3 x_{1} x_{2} - 12 x_{1} - 4 x_{2}^{3} + 7 x_{2}^{2} - 5 x_{2} + 8 \neq 0\), \(x_{1}^{2} x_{2} - 2 x_{1} x_{2}^{3} - 8 x_{1} x_{2}^{2} + 6 x_{1} x_{2} - 2 x_{1} - 12 x_{2}^{3} + 22 x_{2}^{2} - 8 x_{2} \neq 0\), \(x_{1} - x_{2} \neq 0\), \(3 x_{1}^{2} x_{2}^{3} + 12 x_{1}^{2} x_{2}^{2} - 7 x_{1}^{2} x_{2} + x_{1}^{2} + 16 x_{1} x_{2}^{3} - 27 x_{1} x_{2}^{2} + 8 x_{1} x_{2} - x_{2}^{2} \neq 0\), \(x_{1}^{3} - 2 x_{1} x_{2}^{4} - 8 x_{1} x_{2}^{3} + 6 x_{1} x_{2}^{2} - 2 x_{1} x_{2} - 12 x_{2}^{4} + 22 x_{2}^{3} - 8 x_{2}^{2} \neq 0\), \(x_{1}^{2} x_{2} + 4 x_{1}^{2} - x_{1} x_{2}^{3} - 4 x_{1} x_{2}^{2} + 4 x_{1} x_{2} - 8 x_{1} - 4 x_{2}^{3} + 7 x_{2}^{2} + x_{2} \neq 0\), \(3 x_{1} x_{2}^{3} + 12 x_{1} x_{2}^{2} - 7 x_{1} x_{2} + x_{1} + 16 x_{2}^{3} - 27 x_{2}^{2} + 8 x_{2} \neq 0\), \(x_{1} - x_{2}^{2} \neq 0\), \(x_{1}^{2} x_{2} + 4 x_{1}^{2} - x_{1} x_{2}^{3} - 3 x_{1} x_{2}^{2} + 7 x_{1} x_{2} - 10 x_{1} - 4 x_{2}^{3} + 11 x_{2}^{2} - 12 x_{2} + 7 \neq 0\), \(3 x_{1}^{2} x_{2}^{5} + 24 x_{1}^{2} x_{2}^{4} + 47 x_{1}^{2} x_{2}^{3} - 3 x_{1}^{2} x_{2}^{2} - 10 x_{1}^{2} x_{2} + 2 x_{1}^{2} + 28 x_{1} x_{2}^{5} + 64 x_{1} x_{2}^{4} - 183 x_{1} x_{2}^{3} + 18 x_{1} x_{2}^{2} + 12 x_{1} x_{2} - x_{1} + 64 x_{2}^{5} - 220 x_{2}^{4} + 205 x_{2}^{3} - 35 x_{2}^{2} \neq 0\), \(2 x_{1}^{3} x_{2}^{2} + 8 x_{1}^{3} x_{2} + 2 x_{1}^{3} - 3 x_{1}^{2} x_{2}^{4} - 20 x_{1}^{2} x_{2}^{3} - 18 x_{1}^{2} x_{2}^{2} + 7 x_{1}^{2} x_{2} - 9 x_{1}^{2} - 28 x_{1} x_{2}^{4} - 51 x_{1} x_{2}^{3} + 181 x_{1} x_{2}^{2} - 92 x_{1} x_{2} + 16 x_{1} - 72 x_{2}^{4} + 228 x_{2}^{3} - 224 x_{2}^{2} + 64 x_{2} \neq 0\), \(2 x_{1}^{2} x_{2}^{2} + 7 x_{1}^{2} x_{2} - 2 x_{1}^{2} - x_{1} x_{2}^{4} - 4 x_{1} x_{2}^{3} + 8 x_{1} x_{2}^{2} - 21 x_{1} x_{2} + 7 x_{1} - 4 x_{2}^{4} + 7 x_{2}^{3} + x_{2}^{2} \neq 0\), \(3 x_{1}^{2} x_{2}^{4} + 9 x_{1}^{2} x_{2}^{3} - 19 x_{1}^{2} x_{2}^{2} + 8 x_{1}^{2} x_{2} - x_{1}^{2} + 16 x_{1} x_{2}^{4} - 43 x_{1} x_{2}^{3} + 35 x_{1} x_{2}^{2} - 7 x_{1} x_{2} - x_{2}^{3} \neq 0\), \(x_{1}^{2} - 2 x_{1} x_{2}^{3} - 8 x_{1} x_{2}^{2} + 6 x_{1} x_{2} - 2 x_{1} - 12 x_{2}^{3} + 22 x_{2}^{2} - 8 x_{2} \neq 0\), \(x_{1}^{3} - x_{1}^{2} x_{2} - x_{1}^{2} - 2 x_{1} x_{2}^{4} - 6 x_{1} x_{2}^{3} + 15 x_{1} x_{2}^{2} - 8 x_{1} x_{2} + 2 x_{1} - 12 x_{2}^{4} + 34 x_{2}^{3} - 30 x_{2}^{2} + 8 x_{2} \neq 0\), \(3 x_{1}^{3} x_{2}^{4} + 12 x_{1}^{3} x_{2}^{3} - 7 x_{1}^{3} x_{2}^{2} + x_{1}^{3} x_{2} - 6 x_{1}^{2} x_{2}^{6} - 48 x_{1}^{2} x_{2}^{5} - 48 x_{1}^{2} x_{2}^{4} + 93 x_{1}^{2} x_{2}^{3} - 66 x_{1}^{2} x_{2}^{2} + 21 x_{1}^{2} x_{2} - 2 x_{1}^{2} - 68 x_{1} x_{2}^{6} - 152 x_{1} x_{2}^{5} + 620 x_{1} x_{2}^{4} - 521 x_{1} x_{2}^{3} + 180 x_{1} x_{2}^{2} - 24 x_{1} x_{2} - 192 x_{2}^{6} + 676 x_{2}^{5} - 818 x_{2}^{4} + 392 x_{2}^{3} - 64 x_{2}^{2} \neq 0\), \(3 x_{1}^{2} x_{2}^{3} + 12 x_{1}^{2} x_{2}^{2} - 7 x_{1}^{2} x_{2} + x_{1}^{2} + 13 x_{1} x_{2}^{3} - 39 x_{1} x_{2}^{2} + 15 x_{1} x_{2} - x_{1} - 16 x_{2}^{3} + 26 x_{2}^{2} - 7 x_{2} \neq 0\), \(3 x_{1} x_{2}^{3} + 11 x_{1} x_{2}^{2} - 11 x_{1} x_{2} + x_{1} + 16 x_{2}^{3} - 32 x_{2}^{2} + 16 x_{2} \neq 0\), \(2 x_{1}^{2} x_{2}^{4} + 16 x_{1}^{2} x_{2}^{3} + 25 x_{1}^{2} x_{2}^{2} - 26 x_{1}^{2} x_{2} + 7 x_{1}^{2} + 22 x_{1} x_{2}^{4} + 50 x_{1} x_{2}^{3} - 179 x_{1} x_{2}^{2} + 98 x_{1} x_{2} - 16 x_{1} + 60 x_{2}^{4} - 206 x_{2}^{3} + 216 x_{2}^{2} - 64 x_{2} \neq 0\), \(x_{1}^{2} x_{2} + 4 x_{1}^{2} - x_{1} x_{2}^{2} + x_{1} x_{2} - 9 x_{1} - 5 x_{2}^{2} + 8 x_{2} \neq 0\), \(x_{1}^{2} x_{2} + 4 x_{1}^{2} - x_{1} x_{2}^{2} + x_{1} x_{2} - 8 x_{1} - 5 x_{2}^{2} + 7 x_{2} \neq 0\), \(x_{1} x_{2}^{3} + 4 x_{1} x_{2}^{2} - 3 x_{1} x_{2} + x_{1} + 6 x_{2}^{3} - 11 x_{2}^{2} + 4 x_{2} \neq 0\), \(2 \neq 0\), \(3 x_{1}^{2} x_{2}^{3} + 12 x_{1}^{2} x_{2}^{2} - 7 x_{1}^{2} x_{2} + x_{1}^{2} + 15 x_{1} x_{2}^{3} - 31 x_{1} x_{2}^{2} + 8 x_{1} x_{2} - 5 x_{2}^{3} + 7 x_{2}^{2} \neq 0\), \(x_{1}^{3} x_{2}^{2} + 4 x_{1}^{3} x_{2} + x_{1}^{3} - 2 x_{1}^{2} x_{2}^{5} - 16 x_{1}^{2} x_{2}^{4} - 26 x_{1}^{2} x_{2}^{3} + 27 x_{1}^{2} x_{2}^{2} - 16 x_{1}^{2} x_{2} - 22 x_{1} x_{2}^{5} - 52 x_{1} x_{2}^{4} + 166 x_{1} x_{2}^{3} - 84 x_{1} x_{2}^{2} + 14 x_{1} x_{2} - 60 x_{2}^{5} + 194 x_{2}^{4} - 194 x_{2}^{3} + 56 x_{2}^{2} \neq 0\), \(x_{1} x_{2}^{2} + 4 x_{1} x_{2} + x_{1} + 5 x_{2}^{2} - 8 x_{2} \neq 0\), \(3 x_{1}^{2} x_{2}^{3} + 12 x_{1}^{2} x_{2}^{2} - 7 x_{1}^{2} x_{2} + x_{1}^{2} + 15 x_{1} x_{2}^{3} - 31 x_{1} x_{2}^{2} + 7 x_{1} x_{2} - 5 x_{2}^{3} + 8 x_{2}^{2} \neq 0\), \(2 x_{1}^{2} x_{2}^{4} + 16 x_{1}^{2} x_{2}^{3} + 25 x_{1}^{2} x_{2}^{2} - 26 x_{1}^{2} x_{2} + 7 x_{1}^{2} + 22 x_{1} x_{2}^{4} + 52 x_{1} x_{2}^{3} - 171 x_{1} x_{2}^{2} + 92 x_{1} x_{2} - 14 x_{1} + 60 x_{2}^{4} - 194 x_{2}^{3} + 194 x_{2}^{2} - 56 x_{2} \neq 0\), \(6 x_{1}^{2} x_{2}^{6} + 48 x_{1}^{2} x_{2}^{5} + 64 x_{1}^{2} x_{2}^{4} - 121 x_{1}^{2} x_{2}^{3} + 70 x_{1}^{2} x_{2}^{2} - 21 x_{1}^{2} x_{2} + 2 x_{1}^{2} + 68 x_{1} x_{2}^{6} + 152 x_{1} x_{2}^{5} - 620 x_{1} x_{2}^{4} + 515 x_{1} x_{2}^{3} - 172 x_{1} x_{2}^{2} + 24 x_{1} x_{2} + 192 x_{2}^{6} - 676 x_{2}^{5} + 818 x_{2}^{4} - 392 x_{2}^{3} + 64 x_{2}^{2} \neq 0\), \(3 x_{1} x_{2}^{3} + 11 x_{1} x_{2}^{2} - 11 x_{1} x_{2} + x_{1} + 16 x_{2}^{3} - 32 x_{2}^{2} + 15 x_{2} \neq 0\), \(2 x_{1} x_{2}^{3} + 8 x_{1} x_{2}^{2} - 7 x_{1} x_{2} + 2 x_{1} + 12 x_{2}^{3} - 22 x_{2}^{2} + 8 x_{2} \neq 0\), \(x_{1} x_{2}^{2} + 4 x_{1} x_{2} + x_{1} + 4 x_{2}^{2} - 7 x_{2} \neq 0\), \(3 x_{1}^{2} x_{2}^{3} + 12 x_{1}^{2} x_{2}^{2} - 7 x_{1}^{2} x_{2} + x_{1}^{2} - 3 x_{1} x_{2}^{4} + 4 x_{1} x_{2}^{3} - 20 x_{1} x_{2}^{2} + 7 x_{1} x_{2} - 16 x_{2}^{4} + 27 x_{2}^{3} - 9 x_{2}^{2} \neq 0\), \(x_{1}^{3} - x_{1}^{2} x_{2} - 2 x_{1} x_{2}^{4} - 8 x_{1} x_{2}^{3} + 7 x_{1} x_{2}^{2} - 2 x_{1} x_{2} - 12 x_{2}^{4} + 22 x_{2}^{3} - 8 x_{2}^{2} \neq 0\), \(3 x_{1}^{2} x_{2}^{5} + 24 x_{1}^{2} x_{2}^{4} + 44 x_{1}^{2} x_{2}^{3} - 15 x_{1}^{2} x_{2}^{2} - 3 x_{1}^{2} x_{2} + x_{1}^{2} + 28 x_{1} x_{2}^{5} + 64 x_{1} x_{2}^{4} - 196 x_{1} x_{2}^{3} + 57 x_{1} x_{2}^{2} - 3 x_{1} x_{2} + 64 x_{2}^{5} - 220 x_{2}^{4} + 221 x_{2}^{3} - 61 x_{2}^{2} + 8 x_{2} \neq 0\), \(x_{1}^{3} x_{2}^{2} + 4 x_{1}^{3} x_{2} + x_{1}^{3} - 2 x_{1}^{2} x_{2}^{4} - 16 x_{1}^{2} x_{2}^{3} - 21 x_{1}^{2} x_{2}^{2} + 19 x_{1}^{2} x_{2} - 8 x_{1}^{2} - 22 x_{1} x_{2}^{4} - 50 x_{1} x_{2}^{3} + 179 x_{1} x_{2}^{2} - 98 x_{1} x_{2} + 16 x_{1} - 60 x_{2}^{4} + 206 x_{2}^{3} - 216 x_{2}^{2} + 64 x_{2} \neq 0\), \(x_{1}^{2} x_{2}^{2} + 3 x_{1}^{2} x_{2} - 3 x_{1}^{2} + 5 x_{1} x_{2}^{2} - 8 x_{1} x_{2} + 8 x_{1} + 5 x_{2}^{2} - 8 x_{2} \neq 0\), \(3 x_{1}^{2} x_{2}^{3} + 12 x_{1}^{2} x_{2}^{2} - 7 x_{1}^{2} x_{2} + x_{1}^{2} - 3 x_{1} x_{2}^{4} + 4 x_{1} x_{2}^{3} - 20 x_{1} x_{2}^{2} + 6 x_{1} x_{2} - 16 x_{2}^{4} + 27 x_{2}^{3} - 8 x_{2}^{2} \neq 0\), \(6 x_{1}^{2} x_{2}^{6} + 48 x_{1}^{2} x_{2}^{5} + 61 x_{1}^{2} x_{2}^{4} - 132 x_{1}^{2} x_{2}^{3} + 81 x_{1}^{2} x_{2}^{2} - 22 x_{1}^{2} x_{2} + 2 x_{1}^{2} + 68 x_{1} x_{2}^{6} + 152 x_{1} x_{2}^{5} - 636 x_{1} x_{2}^{4} + 547 x_{1} x_{2}^{3} - 188 x_{1} x_{2}^{2} + 24 x_{1} x_{2} + 192 x_{2}^{6} - 676 x_{2}^{5} + 818 x_{2}^{4} - 392 x_{2}^{3} + 64 x_{2}^{2} \neq 0\), \(x_{1} x_{2}^{3} + 4 x_{1} x_{2}^{2} + x_{1} x_{2} + x_{1} + 4 x_{2}^{3} - 7 x_{2}^{2} - x_{2} \neq 0\), \(x_{1}^{2} x_{2}^{3} + 4 x_{1}^{2} x_{2}^{2} + x_{1}^{2} x_{2} + 6 x_{1} x_{2}^{3} + x_{1} x_{2}^{2} - 7 x_{1} x_{2} + 2 x_{1} + 12 x_{2}^{3} - 22 x_{2}^{2} + 8 x_{2} \neq 0\), \(3 x_{1}^{2} x_{2}^{6} + 24 x_{1}^{2} x_{2}^{5} + 44 x_{1}^{2} x_{2}^{4} - 12 x_{1}^{2} x_{2}^{3} + 9 x_{1}^{2} x_{2}^{2} - 6 x_{1}^{2} x_{2} + x_{1}^{2} + 28 x_{1} x_{2}^{6} + 64 x_{1} x_{2}^{5} - 199 x_{1} x_{2}^{4} + 61 x_{1} x_{2}^{3} - 23 x_{1} x_{2}^{2} + 7 x_{1} x_{2} + 64 x_{2}^{6} - 220 x_{2}^{5} + 205 x_{2}^{4} - 34 x_{2}^{3} - x_{2}^{2} \neq 0\), \(x_{1}^{3} x_{2}^{3} + 5 x_{1}^{3} x_{2}^{2} + 5 x_{1}^{3} x_{2} + x_{1}^{3} - 2 x_{1}^{2} x_{2}^{5} - 17 x_{1}^{2} x_{2}^{4} - 26 x_{1}^{2} x_{2}^{3} + 19 x_{1}^{2} x_{2}^{2} - 17 x_{1}^{2} x_{2} - 22 x_{1} x_{2}^{5} - 56 x_{1} x_{2}^{4} + 173 x_{1} x_{2}^{3} - 83 x_{1} x_{2}^{2} + 14 x_{1} x_{2} - 60 x_{2}^{5} + 194 x_{2}^{4} - 194 x_{2}^{3} + 56 x_{2}^{2} \neq 0\), \(3 x_{1}^{3} x_{2}^{3} + 12 x_{1}^{3} x_{2}^{2} - 7 x_{1}^{3} x_{2} + x_{1}^{3} - 6 x_{1}^{2} x_{2}^{6} - 48 x_{1}^{2} x_{2}^{5} - 64 x_{1}^{2} x_{2}^{4} + 136 x_{1}^{2} x_{2}^{3} - 101 x_{1}^{2} x_{2}^{2} + 29 x_{1}^{2} x_{2} - 2 x_{1}^{2} - 68 x_{1} x_{2}^{6} - 152 x_{1} x_{2}^{5} + 620 x_{1} x_{2}^{4} - 520 x_{1} x_{2}^{3} + 179 x_{1} x_{2}^{2} - 24 x_{1} x_{2} - 192 x_{2}^{6} + 676 x_{2}^{5} - 818 x_{2}^{4} + 392 x_{2}^{3} - 64 x_{2}^{2} \neq 0\), \(x_{1} x_{2}^{2} + 3 x_{1} x_{2} - 3 x_{1} + 4 x_{2}^{2} - 12 x_{2} + 7 \neq 0\), \(3 x_{1}^{2} x_{2}^{5} + 24 x_{1}^{2} x_{2}^{4} + 44 x_{1}^{2} x_{2}^{3} - 15 x_{1}^{2} x_{2}^{2} - 3 x_{1}^{2} x_{2} + x_{1}^{2} + 28 x_{1} x_{2}^{5} + 64 x_{1} x_{2}^{4} - 199 x_{1} x_{2}^{3} + 45 x_{1} x_{2}^{2} + 4 x_{1} x_{2} - x_{1} + 64 x_{2}^{5} - 220 x_{2}^{4} + 205 x_{2}^{3} - 34 x_{2}^{2} \neq 0\), \(x_{1}^{3} x_{2}^{2} + 4 x_{1}^{3} x_{2} + x_{1}^{3} - 2 x_{1}^{2} x_{2}^{4} - 17 x_{1}^{2} x_{2}^{3} - 25 x_{1}^{2} x_{2}^{2} + 18 x_{1}^{2} x_{2} - 8 x_{1}^{2} - 22 x_{1} x_{2}^{4} - 56 x_{1} x_{2}^{3} + 178 x_{1} x_{2}^{2} - 91 x_{1} x_{2} + 14 x_{1} - 60 x_{2}^{4} + 194 x_{2}^{3} - 194 x_{2}^{2} + 56 x_{2} \neq 0\), \(3 x_{1}^{3} x_{2}^{6} + 24 x_{1}^{3} x_{2}^{5} + 44 x_{1}^{3} x_{2}^{4} - 15 x_{1}^{3} x_{2}^{3} - 3 x_{1}^{3} x_{2}^{2} + x_{1}^{3} x_{2} + 34 x_{1}^{2} x_{2}^{6} + 112 x_{1}^{2} x_{2}^{5} - 135 x_{1}^{2} x_{2}^{4} - 75 x_{1}^{2} x_{2}^{3} + 78 x_{1}^{2} x_{2}^{2} - 22 x_{1}^{2} x_{2} + 2 x_{1}^{2} + 132 x_{1} x_{2}^{6} - 68 x_{1} x_{2}^{5} - 415 x_{1} x_{2}^{4} + 486 x_{1} x_{2}^{3} - 180 x_{1} x_{2}^{2} + 24 x_{1} x_{2} + 192 x_{2}^{6} - 676 x_{2}^{5} + 818 x_{2}^{4} - 392 x_{2}^{3} + 64 x_{2}^{2} \neq 0\), \(3 x_{1}^{2} x_{2}^{5} + 24 x_{1}^{2} x_{2}^{4} + 44 x_{1}^{2} x_{2}^{3} - 15 x_{1}^{2} x_{2}^{2} - 3 x_{1}^{2} x_{2} + x_{1}^{2} + 28 x_{1} x_{2}^{5} + 64 x_{1} x_{2}^{4} - 196 x_{1} x_{2}^{3} + 57 x_{1} x_{2}^{2} - 3 x_{1} x_{2} + 64 x_{2}^{5} - 220 x_{2}^{4} + 221 x_{2}^{3} - 61 x_{2}^{2} + 7 x_{2} \neq 0\), \(3 x_{1} x_{2}^{3} + 12 x_{1} x_{2}^{2} - 7 x_{1} x_{2} + x_{1} + 16 x_{2}^{3} - 27 x_{2}^{2} + 7 x_{2} \neq 0\), \(6 x_{1}^{2} x_{2}^{6} + 48 x_{1}^{2} x_{2}^{5} + 64 x_{1}^{2} x_{2}^{4} - 120 x_{1}^{2} x_{2}^{3} + 74 x_{1}^{2} x_{2}^{2} - 21 x_{1}^{2} x_{2} + 2 x_{1}^{2} + 68 x_{1} x_{2}^{6} + 152 x_{1} x_{2}^{5} - 620 x_{1} x_{2}^{4} + 520 x_{1} x_{2}^{3} - 180 x_{1} x_{2}^{2} + 24 x_{1} x_{2} + 192 x_{2}^{6} - 676 x_{2}^{5} + 818 x_{2}^{4} - 392 x_{2}^{3} + 64 x_{2}^{2} \neq 0\)
Realization matrix	\(\begin{pmatrix}1 & 0 & x_{1} x_{2} & x_{2} & 1 & 1 & 0 & x_{2} & 0 & 1 & 1 & 1 \\ 1 & x_{2} & 2 x_{1} x_{2}^{3} + 2 x_{1} x_{2}^{2} + 2 x_{1} + 2 x_{2}^{4} + 4 x_{2}^{3} - 8 x_{2}^{2} & x_{1} & 0 & -x_{1} x_{2}^{2} - x_{1} x_{2} - x_{1} - x_{2}^{3} - x_{2}^{2} + 3 x_{2} + 1 & 1 & x_{1} & 0 & 1 & 0 & x_{1} \\ 1 & -x_{1} x_{2} + x_{1} + x_{2}^{5} + x_{2}^{4} + 6 x_{2}^{3} - 5 x_{2}^{2} & x_{1}^{2} & x_{1} & 0 & -x_{1} x_{2} - x_{1} - x_{2}^{2} - 2 x_{2} + 4 & 0 & x_{2} & 1 & 0 & -x_{1} x_{2} - x_{1} - x_{2}^{2} - 2 x_{2} + 4 & x_{2}\end{pmatrix}\)

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

Lines (16)

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