Matroid 2.8.0
| Label | 2.8.0 |
|---|---|
| Id | r2_n8_**************************** |
| Rank | 2 |
| n | 8 |
Basic invariants
Representability
| Characteristic set | not computed |
|---|---|
| Realizable | yes |
| Realizable char0 | not computed |
| Regular | no |
| Binary | no |
| Ternary | no |
| Quaternary | no |
| Graphic | no |
Realization space
Geometry
Other
| Char poly splits | not computed |
|---|---|
| Simplicial arrangement | yes |
| Realization space: n qbar components | 1 |
Tutte polynomial
\(T = x_{0}^{2} + 6 x_{0} + x_{1}^{6} + 2 x_{1}^{5} + 3 x_{1}^{4} + 4 x_{1}^{3} + 5 x_{1}^{2} + 6 x_{1}\)
Combinatorics
Computed on the fly from the id.
Bases (28)
{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} {5,7} {6,7} {1,8} {2,8} {3,8} {4,8} {5,8} {6,8} {7,8}Non-bases (0)
Circuits (56)
{1,2,3} {1,2,4} {1,3,4} {2,3,4} {1,2,5} {1,3,5} {2,3,5} {1,4,5} {2,4,5} {3,4,5} {1,2,6} {1,3,6} {2,3,6} {1,4,6} {2,4,6} {3,4,6} {1,5,6} {2,5,6} {3,5,6} {4,5,6} {1,2,7} {1,3,7} {2,3,7} {1,4,7} {2,4,7} {3,4,7} {1,5,7} {2,5,7} {3,5,7} {4,5,7} {1,6,7} {2,6,7} {3,6,7} {4,6,7} {5,6,7} {1,2,8} {1,3,8} {2,3,8} {1,4,8} {2,4,8} {3,4,8} {1,5,8} {2,5,8} {3,5,8} {4,5,8} {1,6,8} {2,6,8} {3,6,8} {4,6,8} {5,6,8} {1,7,8} {2,7,8} {3,7,8} {4,7,8} {5,7,8} {6,7,8}Flats by rank (10)
- rank 0 (1): {}
- rank 1 (8): {1} {2} {3} {4} {5} {6} {7} {8}
- rank 2 (1): {1,2,3,4,5,6,7,8}
Hyperplanes (8)
{1} {2} {3} {4} {5} {6} {7} {8}Dual (rank 6)
Revlex encoding in this labeling (not canonicalized, so not linked): ****************************
Bases: {3,4,5,6,7,8} {2,4,5,6,7,8} {1,4,5,6,7,8} {2,3,5,6,7,8} {1,3,5,6,7,8} {1,2,5,6,7,8} {2,3,4,6,7,8} {1,3,4,6,7,8} {1,2,4,6,7,8} {1,2,3,6,7,8} {2,3,4,5,7,8} {1,3,4,5,7,8} {1,2,4,5,7,8} {1,2,3,5,7,8} {1,2,3,4,7,8} {2,3,4,5,6,8} {1,3,4,5,6,8} {1,2,4,5,6,8} {1,2,3,5,6,8} {1,2,3,4,6,8} {1,2,3,4,5,8} {2,3,4,5,6,7} {1,3,4,5,6,7} {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: none. Parallel classes of size > 1: none.
Downloads
- Record as JSON
- OSCAR:
matroid_from_revlex_basis_encoding("****************************", 2, 8)