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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 19,501–19,550
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.375429 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.375455 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.375478 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.375482 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.375486 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.375488 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.375523 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.375533 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.375534 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.375558 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.375590 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.375596 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.375656 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.375675 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.375707 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.375717 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.375720 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.375742 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.375773 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.375781 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.375814 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.375817 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.375837 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.375838 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.375918 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.375966 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.376025 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.376051 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.376196 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.376215 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.376227 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.376250 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.376267 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.376287 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.376315 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.376320 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.376337 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.376350 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.376355 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.376381 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.376501 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.376506 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.376518 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.376556 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.376564 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.376572 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.376589 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.376608 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.376609 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.376625 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |