Matroid 2.4.4
| Label | 2.4.4 |
|---|---|
| Id | r2_n4_000*** |
| Rank | 2 |
| n | 4 |
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
\(T = x_{0}^{2} + x_{0} x_{1}^{2} + x_{0} x_{1}\)
Combinatorics
Computed on the fly from the id.
Bases (3)
{1,4} {2,4} {3,4}Non-bases (3)
{1,2} {1,3} {2,3}Circuits (3)
{1,2} {1,3} {2,3}Flats by rank (4)
- rank 0 (1): {}
- rank 1 (2): {1,2,3} {4}
- rank 2 (1): {1,2,3,4}
Hyperplanes (2)
{1,2,3} {4}Dual (rank 2)
Revlex encoding in this labeling (not canonicalized, so not linked): ***000
Bases: {2,3} {1,3} {1,2}
Loops: none. Parallel classes of size > 1: {1,2,3}.
Downloads
- Record as JSON
- OSCAR:
matroid_from_revlex_basis_encoding("000***", 2, 4)