Matroid 3.10.6475
| Label | 3.10.6475 |
|---|---|
| Id | r3_n10_000000*0**00*0**00**00*0**0*0*0****00*0**0***0**0*0*****00*0**0***0****0**0**0***0**00*0**0***0****0****00*0****0******* |
| Rank | 3 |
| n | 10 |
Affine diagram. Loops (not drawn): 1.
Basic invariants
Representability
| Characteristic set | exactly characteristic 2 [2] |
|---|---|
| Realizable | yes |
| Realizable char0 | no |
| Regular | no |
| Binary | no |
| Ternary | no |
| Quaternary | no |
| Graphic | no |
Realization space
| Status | computed_realization_space |
|---|---|
| Dimension of realization space | -1 |
| Expected dimension over ℤ | 3 |
| Components of realization space | unknown |
| Free realization space | no |
| Principal ideal | yes |
| Birational type | empty how determined: birational type method: empty_char0 |
| Birational type components | show[] |
| Good basis | unknown |
| Good basis v2 | 3,4,7 |
Geometry
| Realization space: scheme simple core id | r3_n9_0******0******0*************0******************0*****0****************0*0*********** |
|---|---|
| Smooth char 0 | unknown |
| Singular primes | unknown |
| Realization space: smooth over ℚ | not computed |
| Realization space: smooth over ℤ | yes how determined: smoothness method: simple_core smoothness witness: r3_n9_0******0******0*************0******************0*****0****************0*0*********** |
| Realization space: is regular scheme | yes how determined: regularity method: simple_core regularity witness: r3_n9_0******0******0*************0******************0*****0****************0*0*********** |
| Realization space: singular fiber primes | [] how determined: singular fiber primes method: simple_core |
| Realization space: singular fiber characteristics | not computed |
| Realization space: characteristic dimensions | show[] how determined: characteristic dimensions method: simple_core |
| 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 | 0 |
Tutte polynomial
\(T = x_{0}^{3} x_{1} + 6 x_{0}^{2} x_{1} + 8 x_{0} x_{1}^{2} + 13 x_{0} x_{1} + x_{1}^{7} + 3 x_{1}^{6} + 6 x_{1}^{5} + 10 x_{1}^{4} + 15 x_{1}^{3} + 13 x_{1}^{2}\)
Realization space
| Ring | \(\mathbb{Z}[x_{1}, x_{2}, x_{3}]\) |
|---|---|
| Defining ideal | \(\left(1\right)\) |
| Inequations | \(0 \neq 0\), \(0 \neq 0\), \(0 \neq 0\), \(0 \neq 0\), \(0 \neq 0\), \(0 \neq 0\), \(0 \neq 0\), \(0 \neq 0\), \(0 \neq 0\), \(0 \neq 0\), \(0 \neq 0\), \(0 \neq 0\), \(0 \neq 0\) |
| Realization matrix | none (empty realization space) |
Combinatorics
Computed on the fly from the id.
Bases (76)
{2,3,5} {2,4,5} {3,4,5} {2,3,6} {2,4,6} {3,4,6} {3,5,6} {4,5,6} {2,3,7} {2,4,7} {3,4,7} {2,5,7} {4,5,7} {2,6,7} {3,6,7} {4,6,7} {5,6,7} {2,3,8} {2,4,8} {3,4,8} {2,5,8} {3,5,8} {4,5,8} {2,6,8} {3,6,8} {5,6,8} {2,7,8} {3,7,8} {4,7,8} {5,7,8} {6,7,8} {2,3,9} {2,4,9} {3,4,9} {2,5,9} {3,5,9} {4,5,9} {2,6,9} {3,6,9} {4,6,9} {5,6,9} {2,7,9} {3,7,9} {5,7,9} {6,7,9} {2,8,9} {3,8,9} {4,8,9} {6,8,9} {7,8,9} {2,3,10} {2,4,10} {3,4,10} {2,5,10} {3,5,10} {4,5,10} {2,6,10} {3,6,10} {4,6,10} {5,6,10} {2,7,10} {3,7,10} {4,7,10} {5,7,10} {2,8,10} {4,8,10} {5,8,10} {6,8,10} {7,8,10} {2,9,10} {3,9,10} {4,9,10} {5,9,10} {6,9,10} {7,9,10} {8,9,10}Non-bases (44)
{1,2,3} {1,2,4} {1,3,4} {2,3,4} {1,2,5} {1,3,5} {1,4,5} {1,2,6} {1,3,6} {1,4,6} {1,5,6} {2,5,6} {1,2,7} {1,3,7} {1,4,7} {1,5,7} {3,5,7} {1,6,7} {1,2,8} {1,3,8} {1,4,8} {1,5,8} {1,6,8} {4,6,8} {1,7,8} {1,2,9} {1,3,9} {1,4,9} {1,5,9} {1,6,9} {1,7,9} {4,7,9} {1,8,9} {5,8,9} {1,2,10} {1,3,10} {1,4,10} {1,5,10} {1,6,10} {1,7,10} {6,7,10} {1,8,10} {3,8,10} {1,9,10}Circuits (87)
{1} {2,3,4} {2,5,6} {3,4,5,6} {3,5,7} {2,4,5,7} {2,3,6,7} {2,4,6,7} {3,4,6,7} {4,5,6,7} {2,3,5,8} {2,4,5,8} {3,4,5,8} {2,3,6,8} {4,6,8} {3,5,6,8} {2,3,7,8} {2,4,7,8} {3,4,7,8} {2,5,7,8} {4,5,7,8} {2,6,7,8} {3,6,7,8} {5,6,7,8} {2,3,5,9} {2,4,5,9} {3,4,5,9} {2,3,6,9} {2,4,6,9} {3,4,6,9} {3,5,6,9} {4,5,6,9} {2,3,7,9} {4,7,9} {2,5,7,9} {2,6,7,9} {3,6,7,9} {5,6,7,9} {2,3,8,9} {2,4,8,9} {3,4,8,9} {5,8,9} {2,6,8,9} {3,6,8,9} {2,7,8,9} {3,7,8,9} {6,7,8,9} {2,3,5,10} {2,4,5,10} {3,4,5,10} {2,3,6,10} {2,4,6,10} {3,4,6,10} {3,5,6,10} {4,5,6,10} {2,3,7,10} {2,4,7,10} {3,4,7,10} {2,5,7,10} {4,5,7,10} {6,7,10} {3,8,10} {2,4,8,10} {2,5,8,10} {4,5,8,10} {2,6,8,10} {5,6,8,10} {2,7,8,10} {4,7,8,10} {5,7,8,10} {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} {2,7,9,10} {3,7,9,10} {5,7,9,10} {2,8,9,10} {4,8,9,10} {6,8,9,10} {7,8,9,10}Flats by rank (31)
- rank 0 (1): {1}
- rank 1 (9): {1,2} {1,3} {1,4} {1,5} {1,6} {1,7} {1,8} {1,9} {1,10}
- rank 2 (20): {1,2,3,4} {1,4,5} {1,3,6} {1,2,5,6} {1,2,7} {1,3,5,7} {1,2,8} {1,4,6,8} {1,7,8} {1,2,9} {1,3,9} {1,6,9} {1,4,7,9} {1,5,8,9} {1,2,10} {1,4,10} {1,5,10} {1,6,7,10} {1,3,8,10} {1,9,10}
- rank 3 (1): {1,2,3,4,5,6,7,8,9,10}
Hyperplanes (20)
{1,2,3,4} {1,4,5} {1,3,6} {1,2,5,6} {1,2,7} {1,3,5,7} {1,2,8} {1,4,6,8} {1,7,8} {1,2,9} {1,3,9} {1,6,9} {1,4,7,9} {1,5,8,9} {1,2,10} {1,4,10} {1,5,10} {1,6,7,10} {1,3,8,10} {1,9,10}Lines (8)
{1,2,3,4} {1,2,5,6} {1,3,5,7} {1,4,6,8} {1,4,7,9} {1,5,8,9} {1,6,7,10} {1,3,8,10}Dual (rank 7)
Revlex encoding in this labeling (not canonicalized, so not linked): *******0****0*00****0****0***0**0*00**0***0**0**0****0***0**0*00*****0*0**0***0**0*00****0*0*0**0*00**00**0*00**0*000000
Bases: {1,4,6,7,8,9,10} {1,3,6,7,8,9,10} {1,2,6,7,8,9,10} {1,4,5,7,8,9,10} {1,3,5,7,8,9,10} {1,2,5,7,8,9,10} {1,2,4,7,8,9,10} {1,2,3,7,8,9,10} {1,4,5,6,8,9,10} {1,3,5,6,8,9,10} {1,2,5,6,8,9,10} {1,3,4,6,8,9,10} {1,2,3,6,8,9,10} {1,3,4,5,8,9,10} {1,2,4,5,8,9,10} {1,2,3,5,8,9,10} {1,2,3,4,8,9,10} {1,4,5,6,7,9,10} {1,3,5,6,7,9,10} {1,2,5,6,7,9,10} {1,3,4,6,7,9,10} {1,2,4,6,7,9,10} {1,2,3,6,7,9,10} {1,3,4,5,7,9,10} {1,2,4,5,7,9,10} {1,2,3,4,7,9,10} {1,3,4,5,6,9,10} {1,2,4,5,6,9,10} {1,2,3,5,6,9,10} {1,2,3,4,6,9,10} {1,2,3,4,5,9,10} {1,4,5,6,7,8,10} {1,3,5,6,7,8,10} {1,2,5,6,7,8,10} {1,3,4,6,7,8,10} {1,2,4,6,7,8,10} {1,2,3,6,7,8,10} {1,3,4,5,7,8,10} {1,2,4,5,7,8,10} {1,2,3,5,7,8,10} {1,2,3,4,7,8,10} {1,3,4,5,6,8,10} {1,2,4,5,6,8,10} {1,2,3,4,6,8,10} {1,2,3,4,5,8,10} {1,3,4,5,6,7,10} {1,2,4,5,6,7,10} {1,2,3,5,6,7,10} {1,2,3,4,5,7,10} {1,2,3,4,5,6,10} {1,4,5,6,7,8,9} {1,3,5,6,7,8,9} {1,2,5,6,7,8,9} {1,3,4,6,7,8,9} {1,2,4,6,7,8,9} {1,2,3,6,7,8,9} {1,3,4,5,7,8,9} {1,2,4,5,7,8,9} {1,2,3,5,7,8,9} {1,2,3,4,7,8,9} {1,3,4,5,6,8,9} {1,2,4,5,6,8,9} {1,2,3,5,6,8,9} {1,2,3,4,6,8,9} {1,3,4,5,6,7,9} {1,2,3,5,6,7,9} {1,2,3,4,6,7,9} {1,2,3,4,5,7,9} {1,2,3,4,5,6,9} {1,3,4,5,6,7,8} {1,2,4,5,6,7,8} {1,2,3,5,6,7,8} {1,2,3,4,6,7,8} {1,2,3,4,5,7,8} {1,2,3,4,5,6,8} {1,2,3,4,5,6,7}
Loops: 1. Parallel classes of size > 1: none.
Downloads
- Record as JSON
- OSCAR:
matroid_from_revlex_basis_encoding("000000*0**00*0**00**00*0**0*0*0****00*0**0***0**0*0*****00*0**0***0****0**0**0***0**00*0**0***0****0****00*0****0*******", 3, 10)