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…or describe it by its bases, non-bases or lines
Any labeling of the ground set $\{1,\dots,n\}$ will do: we compute the canonical id.
Sets are written as {1,2,3}, one per line, or, when $n \le 9$, as digit strings such as
123 145. Lines are the lines with at least three points of a simple rank-3 matroid.
A revlex encoding is a string of * and 0.
381,906 matroids, showing 18,651–18,700
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.353571 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.353587 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.353588 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.353590 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.353605 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.353611 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.353613 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.353645 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.353692 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.353724 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.353735 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.353746 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.353771 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.353778 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.353824 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.353841 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.353850 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.353854 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.353914 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.353955 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.353960 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.353984 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.354038 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.354064 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.354076 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.354090 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.354098 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.354103 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.354105 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.354128 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.354139 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.354143 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.354160 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.354161 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.354187 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.354191 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.354198 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.354207 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.354214 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.354285 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.354296 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.354307 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.354315 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.354329 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.354342 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.354375 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.354382 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.354401 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.354485 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.354503 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |