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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 19,951–20,000
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.141292 | 3 | 12 | 208 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.141304 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.141305 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.141320 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.141330 | 3 | 12 | 209 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.141331 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.141343 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.141353 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.141377 | 3 | 12 | 210 | 1 | ✓ | all but 5 | 0 | ? |
| 3.12.141422 | 3 | 12 | 210 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.141434 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.141443 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7,11 | 0 | ? |
| 3.12.141448 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.141450 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.141451 | 3 | 12 | 208 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.141472 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.141478 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.141483 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.141485 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.141496 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.141497 | 3 | 12 | 209 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.141506 | 3 | 12 | 208 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.141525 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7,13 | 0 | ? |
| 3.12.141532 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.141580 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.141583 | 3 | 12 | 208 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.141588 | 3 | 12 | 208 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.141597 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.141600 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.141607 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.141634 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.141635 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.141636 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.141643 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.141656 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,11 | 0 | ? |
| 3.12.141658 | 3 | 12 | 208 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.141669 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.141672 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.141688 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,11 | 0 | ? |
| 3.12.141701 | 3 | 12 | 209 | 1 | ✓ | all but 5 | 0 | ? |
| 3.12.141709 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.141722 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,7,13 | 0 | ? |
| 3.12.141724 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.141738 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.141739 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.141746 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,11 | 0 | ? |
| 3.12.141756 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.141784 | 3 | 12 | 208 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.141809 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.141824 | 3 | 12 | 211 | 1 | ✓ | all but 2,3,5,19 | 0 | ? |