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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 18,751–18,800
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.356421 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.356427 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.356573 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.356606 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.356622 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.356651 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.356699 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.356737 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.356747 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.356752 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.356755 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.356800 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.356978 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.356984 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.356991 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.357009 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.357017 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.357164 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.357169 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.357189 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.357193 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.357208 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.357215 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.357263 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.357295 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.357296 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.357313 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.357330 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.357342 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.357394 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.357415 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.357426 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.357428 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.357432 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.357435 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.357453 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.357477 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.357542 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.357605 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.357638 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.357668 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.357703 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.357746 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.357756 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.357805 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.357837 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.357902 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.357913 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.357925 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.357930 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |