Matroid 3.3.0
| Label | 3.3.0 |
|---|---|
| Id | r3_n3_* |
| Rank | 3 |
| n | 3 |
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 | 1 |
| 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 |
Geometry
| Realization space: scheme simple core id | r3_n3_* |
|---|---|
| Smooth char 0 | not computed |
| Singular primes | not computed |
| Realization space: smooth over ℚ | not computed |
| Realization space: smooth over ℤ | yes how determined: smoothness method: simple_disconnected_open_affine |
| Realization space: is regular scheme | yes how determined: regularity method: simple_disconnected_open_affine |
| Realization space: singular fiber primes | [] how determined: singular fiber primes method: smooth_over_ZZ |
| Realization space: singular fiber characteristics | not computed |
| Realization space: characteristic dimensions | show[
{
"p": 0,
"d": 0
}
]how determined: characteristic dimensions method: cofinite_smooth_equidimensional |
| Realization space: characteristic dimension unexpected | no |
| Realization space: characteristic dimension varies | no |
Other
| Char poly splits | true |
|---|---|
| Simplicial arrangement | yes |
| Realization space: n qbar components | 1 |
Tutte polynomial
\(T = x^{3}\)
Realization space
| Ring | \(\mathbb{Z}\) |
|---|---|
| Defining ideal | \(\left(0\right)\) |
| Inequations | none |
| Realization matrix | \(\begin{pmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{pmatrix}\) |
Combinatorics
Computed on the fly from the id.
Bases (1)
{1,2,3}Non-bases (0)
Circuits (0)
Flats by rank (8)
- rank 0 (1): {}
- rank 1 (3): {1} {2} {3}
- rank 2 (3): {1,2} {1,3} {2,3}
- rank 3 (1): {1,2,3}
Hyperplanes (3)
{1,2} {1,3} {2,3}Lines (0)
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("*", 3, 3)