Matroid 3.7.13
| Label | 3.7.13 |
|---|---|
| Id | r3_n7_0******0******0***0******0*0**0**** |
| Rank | 3 |
| 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 | 0 |
| Components of realization space | 0 |
| Free realization space | no |
| Principal ideal | yes |
| Birational type | empty how determined: birational type method: empty_char0 |
| Birational type components | show[] |
| Good basis | 1,2,4 |
| Good basis v2 | 1,2,4 |
Geometry
| Realization space: scheme simple core id | r3_n7_0******0******0***0******0*0**0**** |
|---|---|
| Smooth char 0 | yes |
| Singular primes | [] |
| Realization space: smooth over ℚ | not computed |
| Realization space: smooth over ℤ | no how determined: smoothness method: nonflat_vertical |
| Realization space: is regular scheme | yes how determined: regularity method: direct_vertical_fiber_jacobian |
| Realization space: singular fiber primes | [] how determined: singular fiber primes method: direct_vertical_fiber_jacobian |
| Realization space: singular fiber characteristics | not computed |
| Realization space: characteristic dimensions | show[
{
"p": 2,
"d": 0
}
]how determined: characteristic dimensions method: finite_exact_fiber_saturation |
| Realization space: characteristic dimension unexpected | yes |
| Realization space: characteristic dimension varies | no |
Other
| Char poly splits | true |
|---|---|
| Simplicial arrangement | no |
| Realization space: n qbar components | 0 |
Tutte polynomial
\(T = x_{0}^{3} + 4 x_{0}^{2} + 7 x_{0} x_{1} + 3 x_{0} + x_{1}^{4} + 3 x_{1}^{3} + 6 x_{1}^{2} + 3 x_{1}\)
Realization space
| Ring | \(\mathbb{Z}\) |
|---|---|
| Defining ideal | \(\left(2\right)\) |
| Inequations | none |
| Realization matrix | \(\begin{pmatrix}1 & 0 & 1 & 0 & 1 & 0 & 1 \\ 0 & 1 & 1 & 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 1 & 1 & 1 & 1\end{pmatrix}\) |
Combinatorics
Computed on the fly from the id.
Bases (28)
{1,2,4} {1,3,4} {2,3,4} {1,2,5} {1,3,5} {2,3,5} {2,4,5} {3,4,5} {1,2,6} {1,3,6} {2,3,6} {1,4,6} {3,4,6} {1,5,6} {2,5,6} {4,5,6} {1,2,7} {1,3,7} {2,3,7} {1,4,7} {2,4,7} {1,5,7} {3,5,7} {4,5,7} {2,6,7} {3,6,7} {4,6,7} {5,6,7}Non-bases (7)
{1,2,3} {1,4,5} {2,4,6} {3,5,6} {3,4,7} {2,5,7} {1,6,7}Circuits (14)
{1,2,3} {1,4,5} {2,3,4,5} {2,4,6} {1,3,4,6} {1,2,5,6} {3,5,6} {1,2,4,7} {3,4,7} {2,5,7} {1,3,5,7} {1,6,7} {2,3,6,7} {4,5,6,7}Flats by rank (16)
- rank 0 (1): {}
- rank 1 (7): {1} {2} {3} {4} {5} {6} {7}
- rank 2 (7): {1,2,3} {1,4,5} {2,4,6} {3,5,6} {3,4,7} {2,5,7} {1,6,7}
- rank 3 (1): {1,2,3,4,5,6,7}
Hyperplanes (7)
{1,2,3} {1,4,5} {2,4,6} {3,5,6} {3,4,7} {2,5,7} {1,6,7}Lines (7)
{1,2,3} {1,4,5} {2,4,6} {3,5,6} {3,4,7} {2,5,7} {1,6,7}Dual (rank 4)
Revlex encoding in this labeling (not canonicalized, so not linked): ****0**0*0******0***0******0******0
Bases: {3,5,6,7} {2,5,6,7} {1,5,6,7} {3,4,6,7} {2,4,6,7} {1,4,6,7} {1,3,6,7} {1,2,6,7} {3,4,5,7} {2,4,5,7} {1,4,5,7} {2,3,5,7} {1,2,5,7} {2,3,4,7} {1,3,4,7} {1,2,3,7} {3,4,5,6} {2,4,5,6} {1,4,5,6} {2,3,5,6} {1,3,5,6} {2,3,4,6} {1,2,4,6} {1,2,3,6} {1,3,4,5} {1,2,4,5} {1,2,3,5} {1,2,3,4}
Loops: none. Parallel classes of size > 1: none.
Downloads
- Record as JSON
- OSCAR:
matroid_from_revlex_basis_encoding("0******0******0***0******0*0**0****", 3, 7)