Matroid 2.8.44
| Label | 2.8.44 |
|---|---|
| Id | r2_n8_00000000000000000****00***** |
| 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
\(T = x_{0}^{2} x_{1}^{2} + x_{0} x_{1}^{5} + x_{0} x_{1}^{4} + x_{0} x_{1}^{3} + x_{0} x_{1}^{2} + x_{1}^{6} + x_{1}^{5} + x_{1}^{4} + x_{1}^{3}\)
Combinatorics
Computed on the fly from the id.
Bases (9)
{3,7} {4,7} {5,7} {6,7} {3,8} {4,8} {5,8} {6,8} {7,8}Non-bases (19)
{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} {1,8} {2,8}Circuits (12)
{1} {2} {3,4} {3,5} {4,5} {3,6} {4,6} {5,6} {3,7,8} {4,7,8} {5,7,8} {6,7,8}Flats by rank (5)
- rank 0 (1): {1,2}
- rank 1 (3): {1,2,3,4,5,6} {1,2,7} {1,2,8}
- rank 2 (1): {1,2,3,4,5,6,7,8}
Hyperplanes (3)
{1,2,3,4,5,6} {1,2,7} {1,2,8}Dual (rank 6)
Revlex encoding in this labeling (not canonicalized, so not linked): *****00****00000000000000000
Bases: {1,2,4,5,6,8} {1,2,3,5,6,8} {1,2,3,4,6,8} {1,2,3,4,5,8} {1,2,4,5,6,7} {1,2,3,5,6,7} {1,2,3,4,6,7} {1,2,3,4,5,7} {1,2,3,4,5,6}
Loops: 1, 2. Parallel classes of size > 1: {3,4,5,6}.
Downloads
- Record as JSON
- OSCAR:
matroid_from_revlex_basis_encoding("00000000000000000****00*****", 2, 8)