Matroid 4.7.13
| Label | 4.7.13 |
|---|---|
| Id | r4_n7_0********0****0*****0**0***00****** |
| Rank | 4 |
| n | 7 |
Basic invariants
Representability
| Characteristic set | exactly characteristic 2 [2] |
|---|---|
| Realizable | yes |
| Realizable char0 | no |
| Regular | no |
| Binary | yes |
| Ternary | no |
| Quaternary | yes |
| Graphic | no |
Realization space
| Status | computed_realization_space |
|---|---|
| Dimension of realization space | -1 |
| Expected dimension over ℤ | not computed |
| Components of realization space | 1 |
| Free realization space | no |
| Principal ideal | yes |
| Birational type | empty how determined: birational type method: empty_char0 |
| Birational type components | show[] |
| Good basis | not computed |
| Good basis v2 | 1,2,3,5 |
Geometry
Other
| Char poly splits | false |
|---|---|
| Simplicial arrangement | no |
| Realization space: n qbar components | 0 |
Tutte polynomial
\(T = x^{4} + 3 x^{3} + 6 x^{2} + 7 x y + 3 x + y^{3} + 4 y^{2} + 3 y\)
Realization space
| Ring | \(\mathbb{Z}\) |
|---|---|
| Defining ideal | \(\left(2\right)\) |
| Inequations | none |
| Realization matrix | \(\begin{pmatrix}1 & 0 & 0 & 1 & 0 & 1 & 1 \\ 0 & 1 & 0 & 1 & 0 & 1 & 0 \\ 0 & 0 & 1 & 1 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 1 & 1 & 1\end{pmatrix}\) |
Combinatorics
Computed on the fly from the id.
Bases (28)
{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} {2,3,4,6} {1,3,5,6} {2,3,5,6} {1,4,5,6} {2,4,5,6} {1,2,3,7} {1,2,4,7} {1,3,4,7} {2,3,4,7} {1,2,5,7} {2,3,5,7} {1,4,5,7} {3,4,5,7} {1,2,6,7} {1,3,6,7} {2,4,6,7} {3,4,6,7} {1,5,6,7} {2,5,6,7} {3,5,6,7} {4,5,6,7}Non-bases (7)
{1,2,3,4} {1,2,5,6} {3,4,5,6} {1,3,5,7} {2,4,5,7} {2,3,6,7} {1,4,6,7}Circuits (7)
{1,2,3,4} {1,2,5,6} {3,4,5,6} {1,3,5,7} {2,4,5,7} {2,3,6,7} {1,4,6,7}Flats by rank (44)
- rank 0 (1): {}
- rank 1 (7): {1} {2} {3} {4} {5} {6} {7}
- rank 2 (21): {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}
- rank 3 (14): {1,2,3,4} {2,3,5} {1,4,5} {1,3,6} {2,4,6} {1,2,5,6} {3,4,5,6} {1,2,7} {3,4,7} {1,3,5,7} {2,4,5,7} {2,3,6,7} {1,4,6,7} {5,6,7}
- rank 4 (1): {1,2,3,4,5,6,7}
Hyperplanes (14)
{1,2,3,4} {2,3,5} {1,4,5} {1,3,6} {2,4,6} {1,2,5,6} {3,4,5,6} {1,2,7} {3,4,7} {1,3,5,7} {2,4,5,7} {2,3,6,7} {1,4,6,7} {5,6,7}Dual (rank 3)
Revlex encoding in this labeling (not canonicalized, so not linked): ******00***0**0*****0****0********0
Bases: {4,6,7} {3,6,7} {2,6,7} {1,6,7} {4,5,7} {3,5,7} {2,5,7} {1,5,7} {2,4,7} {1,4,7} {2,3,7} {1,3,7} {4,5,6} {3,5,6} {2,5,6} {1,5,6} {3,4,6} {1,4,6} {2,3,6} {1,2,6} {3,4,5} {2,4,5} {1,3,5} {1,2,5} {2,3,4} {1,3,4} {1,2,4} {1,2,3}
Loops: none. Parallel classes of size > 1: none.
Downloads
- Record as JSON
- OSCAR:
matroid_from_revlex_basis_encoding("0********0****0*****0**0***00******", 4, 7)