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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 19,301–19,350
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.370461 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.370490 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.370491 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.370499 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.370518 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.370527 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.370550 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.370551 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.370562 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.370564 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.370578 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.370618 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.370678 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.370685 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.370715 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.370790 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.370796 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.370891 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.370908 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.371003 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.371052 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.371071 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.371073 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.371076 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.371094 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.371114 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.371156 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.371173 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.371283 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.371304 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.371308 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.371359 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.371363 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.371367 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.371386 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.371463 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.371471 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.371479 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.371507 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.371515 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.371564 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.371610 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.371795 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.371913 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.371949 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.372064 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.372194 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.372300 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.372319 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.372357 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |