Matroid 4.4.0
| Label | 4.4.0 |
|---|---|
| Id | r4_n4_* |
| Rank | 4 |
| n | 4 |
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 | not computed |
| 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 | 1,2,3,4 |
Geometry
Other
| Char poly splits | true |
|---|---|
| Simplicial arrangement | yes |
| Realization space: n qbar components | 1 |
Tutte polynomial
\(T = x^{4}\)
Realization space
| Ring | \(\mathbb{Z}\) |
|---|---|
| Defining ideal | \(\left(0\right)\) |
| Inequations | none |
| Realization matrix | \(\begin{pmatrix}1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{pmatrix}\) |
Combinatorics
Computed on the fly from the id.
Bases (1)
{1,2,3,4}Non-bases (0)
Circuits (0)
Flats by rank (16)
- rank 0 (1): {}
- rank 1 (4): {1} {2} {3} {4}
- rank 2 (6): {1,2} {1,3} {2,3} {1,4} {2,4} {3,4}
- rank 3 (4): {1,2,3} {1,2,4} {1,3,4} {2,3,4}
- rank 4 (1): {1,2,3,4}
Hyperplanes (4)
{1,2,3} {1,2,4} {1,3,4} {2,3,4}Dual (rank 0)
Revlex encoding in this labeling (not canonicalized, so not linked): *
Bases: {}
Loops: none. Parallel classes of size > 1: none.
Downloads
- Record as JSON
- OSCAR:
matroid_from_revlex_basis_encoding("*", 4, 4)