Matroid 2.5.7
| Label | 2.5.7 |
|---|---|
| Id | r2_n5_0000**0**0 |
| Rank | 2 |
| n | 5 |
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
\(T = x_{0}^{2} x_{1} + 2 x_{0} x_{1}^{2} + x_{1}^{3}\)
Combinatorics
Computed on the fly from the id.
Bases (4)
{2,4} {3,4} {2,5} {3,5}Non-bases (6)
{1,2} {1,3} {2,3} {1,4} {1,5} {4,5}Circuits (3)
{1} {2,3} {4,5}Flats by rank (4)
- rank 0 (1): {1}
- rank 1 (2): {1,2,3} {1,4,5}
- rank 2 (1): {1,2,3,4,5}
Hyperplanes (2)
{1,2,3} {1,4,5}Dual (rank 3)
Revlex encoding in this labeling (not canonicalized, so not linked): 0**0**0000
Bases: {1,3,5} {1,2,5} {1,3,4} {1,2,4}
Loops: 1. Parallel classes of size > 1: {2,3} {4,5}.
Downloads
- Record as JSON
- OSCAR:
matroid_from_revlex_basis_encoding("0000**0**0", 2, 5)