Matroid 4.7.51
| Label | 4.7.51 |
|---|---|
| Id | r4_n7_00000000*00*0**000*00*0**0000**0**0 |
| Rank | 4 |
| n | 7 |
A graph with this cycle matroid; edge labels are elements.
Basic invariants
Representability
| Characteristic set | characteristic 0 and all primes [0] |
|---|---|
| Realizable | yes |
| Realizable char0 | yes |
| Regular | yes |
| Binary | yes |
| Ternary | yes |
| Quaternary | yes |
| Graphic | yes |
Realization space
| Status | computed_realization_space |
|---|---|
| Dimension of realization space | 0 |
| Expected dimension over ℤ | not computed |
| Components of realization space | 1 |
| Free realization space | yes |
| Principal ideal | yes |
| Birational type | rational how determined: birational type method: rigid |
| Birational type components | show[
{
"dim": 0,
"free_rank": 0,
"torus_rank": 0,
"core_dim": 0,
"qbar_components": 1,
"type": "rational",
"reason": "rigid: unique realization over Q (integer matrix)"
}
] |
| Good basis | not computed |
| Good basis v2 | 2,3,4,6 |
Geometry
Other
| Char poly splits | false |
|---|---|
| Simplicial arrangement | no |
| Realization space: n qbar components | 1 |
Tutte polynomial
\(T = x^{4} y + 2 x^{3} y + 3 x^{2} y + 3 x y^{2} + x y + y^{3} + y^{2}\)
Realization space
| Ring | \(\mathbb{Z}\) |
|---|---|
| Defining ideal | \(\left(0\right)\) |
| Inequations | none |
| Realization matrix | \(\begin{pmatrix}0 & 1 & 0 & 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & 0 & 1 & 0 & 1 \\ 0 & 0 & 0 & 1 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1\end{pmatrix}\) |
Combinatorics
Computed on the fly from the id.
Bases (12)
{2,3,4,6} {2,3,5,6} {2,4,5,6} {3,4,5,6} {2,3,4,7} {2,3,5,7} {2,4,5,7} {3,4,5,7} {2,4,6,7} {3,4,6,7} {2,5,6,7} {3,5,6,7}Non-bases (23)
{1,2,3,4} {1,2,3,5} {1,2,4,5} {1,3,4,5} {2,3,4,5} {1,2,3,6} {1,2,4,6} {1,3,4,6} {1,2,5,6} {1,3,5,6} {1,4,5,6} {1,2,3,7} {1,2,4,7} {1,3,4,7} {1,2,5,7} {1,3,5,7} {1,4,5,7} {1,2,6,7} {1,3,6,7} {2,3,6,7} {1,4,6,7} {1,5,6,7} {4,5,6,7}Circuits (4)
{1} {2,3,4,5} {2,3,6,7} {4,5,6,7}Flats by rank (34)
- rank 0 (1): {1}
- rank 1 (6): {1,2} {1,3} {1,4} {1,5} {1,6} {1,7}
- rank 2 (15): {1,2,3} {1,2,4} {1,3,4} {1,2,5} {1,3,5} {1,4,5} {1,2,6} {1,3,6} {1,4,6} {1,5,6} {1,2,7} {1,3,7} {1,4,7} {1,5,7} {1,6,7}
- rank 3 (11): {1,2,3,4,5} {1,2,4,6} {1,3,4,6} {1,2,5,6} {1,3,5,6} {1,2,4,7} {1,3,4,7} {1,2,5,7} {1,3,5,7} {1,2,3,6,7} {1,4,5,6,7}
- rank 4 (1): {1,2,3,4,5,6,7}
Hyperplanes (11)
{1,2,3,4,5} {1,2,4,6} {1,3,4,6} {1,2,5,6} {1,3,5,6} {1,2,4,7} {1,3,4,7} {1,2,5,7} {1,3,5,7} {1,2,3,6,7} {1,4,5,6,7}Dual (rank 3)
Revlex encoding in this labeling (not canonicalized, so not linked): 0**0**0000**0*00*000**0*00*00000000
Bases: {1,5,7} {1,4,7} {1,3,7} {1,2,7} {1,5,6} {1,4,6} {1,3,6} {1,2,6} {1,3,5} {1,2,5} {1,3,4} {1,2,4}
Loops: 1. Parallel classes of size > 1: none.
Downloads
- Record as JSON
- OSCAR:
matroid_from_revlex_basis_encoding("00000000*00*0**000*00*0**0000**0**0", 4, 7)