Matroid 3.11.298473
| Label | 3.11.298473 |
|---|---|
| Id | r3_n11_0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000*****000****** |
| Rank | 3 |
| n | 11 |
Affine diagram (real realization). Loops (not drawn): 1, 2, 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 | 2 |
| 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 | unknown |
| Good basis v2 | 4,9,11 |
Geometry
Other
| Char poly splits | true |
|---|---|
| Simplicial arrangement | yes |
| Realization space: n qbar components | not computed |
Tutte polynomial
\(T = x_{0}^{3} x_{1}^{3} + x_{0}^{2} x_{1}^{7} + x_{0}^{2} x_{1}^{6} + x_{0}^{2} x_{1}^{5} + x_{0}^{2} x_{1}^{4} + x_{0}^{2} x_{1}^{3} + x_{0} x_{1}^{8} + x_{0} x_{1}^{7} + x_{0} x_{1}^{6} + x_{0} x_{1}^{5} + x_{0} x_{1}^{4}\)
Realization space
| Ring | \(\mathbb{Z}\) |
|---|---|
| Defining ideal | \(\left(0\right)\) |
| Inequations | none |
| Realization matrix | \(\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}\) |
Combinatorics
Computed on the fly from the id.
Bases (11)
{4,9,11} {5,9,11} {6,9,11} {7,9,11} {8,9,11} {4,10,11} {5,10,11} {6,10,11} {7,10,11} {8,10,11} {9,10,11}Non-bases (154)
{1,2,3} {1,2,4} {1,3,4} {2,3,4} {1,2,5} {1,3,5} {2,3,5} {1,4,5} {2,4,5} {3,4,5} {1,2,6} {1,3,6} {2,3,6} {1,4,6} {2,4,6} {3,4,6} {1,5,6} {2,5,6} {3,5,6} {4,5,6} {1,2,7} {1,3,7} {2,3,7} {1,4,7} {2,4,7} {3,4,7} {1,5,7} {2,5,7} {3,5,7} {4,5,7} {1,6,7} {2,6,7} {3,6,7} {4,6,7} {5,6,7} {1,2,8} {1,3,8} {2,3,8} {1,4,8} {2,4,8} {3,4,8} {1,5,8} {2,5,8} {3,5,8} {4,5,8} {1,6,8} {2,6,8} {3,6,8} {4,6,8} {5,6,8} {1,7,8} {2,7,8} {3,7,8} {4,7,8} {5,7,8} {6,7,8} {1,2,9} {1,3,9} {2,3,9} {1,4,9} {2,4,9} {3,4,9} {1,5,9} {2,5,9} {3,5,9} {4,5,9} {1,6,9} {2,6,9} {3,6,9} {4,6,9} {5,6,9} {1,7,9} {2,7,9} {3,7,9} {4,7,9} {5,7,9} {6,7,9} {1,8,9} {2,8,9} {3,8,9} {4,8,9} {5,8,9} {6,8,9} {7,8,9} {1,2,10} {1,3,10} {2,3,10} {1,4,10} {2,4,10} {3,4,10} {1,5,10} {2,5,10} {3,5,10} {4,5,10} {1,6,10} {2,6,10} {3,6,10} {4,6,10} {5,6,10} {1,7,10} {2,7,10} {3,7,10} {4,7,10} {5,7,10} {6,7,10} {1,8,10} {2,8,10} {3,8,10} {4,8,10} {5,8,10} {6,8,10} {7,8,10} {1,9,10} {2,9,10} {3,9,10} {4,9,10} {5,9,10} {6,9,10} {7,9,10} {8,9,10} {1,2,11} {1,3,11} {2,3,11} {1,4,11} {2,4,11} {3,4,11} {1,5,11} {2,5,11} {3,5,11} {4,5,11} {1,6,11} {2,6,11} {3,6,11} {4,6,11} {5,6,11} {1,7,11} {2,7,11} {3,7,11} {4,7,11} {5,7,11} {6,7,11} {1,8,11} {2,8,11} {3,8,11} {4,8,11} {5,8,11} {6,8,11} {7,8,11} {1,9,11} {2,9,11} {3,9,11} {1,10,11} {2,10,11} {3,10,11}Circuits (18)
{1} {2} {3} {4,5} {4,6} {5,6} {4,7} {5,7} {6,7} {4,8} {5,8} {6,8} {7,8} {4,9,10} {5,9,10} {6,9,10} {7,9,10} {8,9,10}Flats by rank (10)
- rank 0 (1): {1,2,3}
- rank 1 (4): {1,2,3,4,5,6,7,8} {1,2,3,9} {1,2,3,10} {1,2,3,11}
- rank 2 (4): {1,2,3,4,5,6,7,8,9,10} {1,2,3,4,5,6,7,8,11} {1,2,3,9,11} {1,2,3,10,11}
- rank 3 (1): {1,2,3,4,5,6,7,8,9,10,11}
Hyperplanes (4)
{1,2,3,4,5,6,7,8,9,10} {1,2,3,4,5,6,7,8,11} {1,2,3,9,11} {1,2,3,10,11}Lines (1)
{1,2,3,4,5,6,7,8,9,10}Dual (rank 8)
Revlex encoding in this labeling (not canonicalized, so not linked): ******000*****0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Bases: {1,2,3,5,6,7,8,10} {1,2,3,4,6,7,8,10} {1,2,3,4,5,7,8,10} {1,2,3,4,5,6,8,10} {1,2,3,4,5,6,7,10} {1,2,3,5,6,7,8,9} {1,2,3,4,6,7,8,9} {1,2,3,4,5,7,8,9} {1,2,3,4,5,6,8,9} {1,2,3,4,5,6,7,9} {1,2,3,4,5,6,7,8}
Loops: 1, 2, 3. Parallel classes of size > 1: {4,5,6,7,8}.
Downloads
- Record as JSON
- OSCAR:
matroid_from_revlex_basis_encoding("0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000*****000******", 3, 11)