Matroid 2.8.49
| Label | 2.8.49 |
|---|---|
| Id | r2_n8_0000000000000000000**0000**0 |
| Rank | 2 |
| n | 8 |
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
\(T = x_{0}^{2} x_{1}^{4} + 2 x_{0} x_{1}^{5} + x_{1}^{6}\)
Combinatorics
Computed on the fly from the id.
Bases (4)
{5,7} {6,7} {5,8} {6,8}Non-bases (24)
{1,2} {1,3} {2,3} {1,4} {2,4} {3,4} {1,5} {2,5} {3,5} {4,5} {1,6} {2,6} {3,6} {4,6} {5,6} {1,7} {2,7} {3,7} {4,7} {1,8} {2,8} {3,8} {4,8} {7,8}Circuits (6)
{1} {2} {3} {4} {5,6} {7,8}Flats by rank (4)
- rank 0 (1): {1,2,3,4}
- rank 1 (2): {1,2,3,4,5,6} {1,2,3,4,7,8}
- rank 2 (1): {1,2,3,4,5,6,7,8}
Hyperplanes (2)
{1,2,3,4,5,6} {1,2,3,4,7,8}Dual (rank 6)
Revlex encoding in this labeling (not canonicalized, so not linked): 0**0000**0000000000000000000
Bases: {1,2,3,4,6,8} {1,2,3,4,5,8} {1,2,3,4,6,7} {1,2,3,4,5,7}
Loops: 1, 2, 3, 4. Parallel classes of size > 1: {5,6} {7,8}.
Downloads
- Record as JSON
- OSCAR:
matroid_from_revlex_basis_encoding("0000000000000000000**0000**0", 2, 8)