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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.
2,030,492 matroids, showing 19,151–19,200
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.130176 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,11 | 0 | ? |
| 3.12.130185 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.130194 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.130202 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.130210 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.130293 | 3 | 12 | 210 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.130303 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.130318 | 3 | 12 | 209 | 2 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.130342 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.130347 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.130360 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.130373 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.130381 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.130383 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.130398 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.130402 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.130404 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.130414 | 3 | 12 | 208 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.130465 | 3 | 12 | 209 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.130468 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.130471 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.130473 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.130474 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.130495 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.130496 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.130509 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.130518 | 3 | 12 | 208 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.130526 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.130530 | 3 | 12 | 210 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.130534 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.130559 | 3 | 12 | 208 | 1 | ✓ | all but 5 | 0 | ? |
| 3.12.130575 | 3 | 12 | 208 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.130580 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,13 | 0 | ? |
| 3.12.130614 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.130652 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.130664 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.130669 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.130689 | 3 | 12 | 209 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.130690 | 3 | 12 | 208 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.130699 | 3 | 12 | 208 | 1 | ✓ | all but 5 | 0 | ? |
| 3.12.130703 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.130718 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.130721 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.130750 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.130753 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.130766 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.130774 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.130785 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.130790 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7,11,13 | 0 | ? |
| 3.12.130793 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |