Matroid 2.7.8
| Label | 2.7.8 |
|---|---|
| Id | r2_n7_000******0***00****** |
| Rank | 2 |
| n | 7 |
A graph with this cycle matroid; edge labels are elements.
Basic invariants
Representability
| Characteristic set | not computed |
|---|---|
| Realizable | yes |
| Realizable char0 | not computed |
| Regular | yes |
| Binary | yes |
| Ternary | yes |
| Quaternary | yes |
| Graphic | yes |
Realization space
Geometry
Other
| Char poly splits | not computed |
|---|---|
| Simplicial arrangement | yes |
| Realization space: n qbar components | 1 |
Tutte polynomial
\(T = x_{0}^{2} + 2 x_{0} x_{1}^{2} + 2 x_{0} x_{1} + x_{0} + x_{1}^{5} + 2 x_{1}^{4} + 3 x_{1}^{3} + 2 x_{1}^{2} + x_{1}\)
Combinatorics
Computed on the fly from the id.
Bases (15)
{1,4} {2,4} {3,4} {1,5} {2,5} {3,5} {1,6} {2,6} {3,6} {1,7} {2,7} {3,7} {4,7} {5,7} {6,7}Non-bases (6)
{1,2} {1,3} {2,3} {4,5} {4,6} {5,6}Circuits (15)
{1,2} {1,3} {2,3} {4,5} {4,6} {5,6} {1,4,7} {2,4,7} {3,4,7} {1,5,7} {2,5,7} {3,5,7} {1,6,7} {2,6,7} {3,6,7}Flats by rank (5)
- rank 0 (1): {}
- rank 1 (3): {1,2,3} {4,5,6} {7}
- rank 2 (1): {1,2,3,4,5,6,7}
Hyperplanes (3)
{1,2,3} {4,5,6} {7}Dual (rank 5)
Revlex encoding in this labeling (not canonicalized, so not linked): ******00***0******000
Bases: {2,3,5,6,7} {1,3,5,6,7} {1,2,5,6,7} {2,3,4,6,7} {1,3,4,6,7} {1,2,4,6,7} {2,3,4,5,7} {1,3,4,5,7} {1,2,4,5,7} {2,3,4,5,6} {1,3,4,5,6} {1,2,4,5,6} {1,2,3,5,6} {1,2,3,4,6} {1,2,3,4,5}
Loops: none. Parallel classes of size > 1: {1,2,3} {4,5,6}.
Downloads
- Record as JSON
- OSCAR:
matroid_from_revlex_basis_encoding("000******0***00******", 2, 7)