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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 22,201–22,250
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.172325 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.172338 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,11,23 | 0 | ? |
| 3.12.172354 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.172376 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,13 | 0 | ? |
| 3.12.172384 | 3 | 12 | 210 | 1 | ✓ | all but 7 | 0 | ? |
| 3.12.172394 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.172412 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.172414 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.172421 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.172433 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.172442 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.172446 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.172460 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.172465 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.172469 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.172491 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.172502 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.172504 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.172505 | 3 | 12 | 209 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.172521 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,11 | 0 | ? |
| 3.12.172537 | 3 | 12 | 207 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.172540 | 3 | 12 | 207 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.172548 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.172554 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.172555 | 3 | 12 | 207 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.172559 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.172561 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.172579 | 3 | 12 | 208 | 1 | ✓ | all but 2,11 | 0 | ? |
| 3.12.172580 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.172583 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.172590 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.172595 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,11 | 0 | ? |
| 3.12.172598 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.172613 | 3 | 12 | 209 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.172621 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,7,17 | 0 | ? |
| 3.12.172622 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.172635 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.172640 | 3 | 12 | 208 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.172644 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.172645 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.172652 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.172683 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.172686 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.172689 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.172692 | 3 | 12 | 207 | 2 | ✓ | all but 2,5 | 0 | ? |
| 3.12.172700 | 3 | 12 | 208 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.172702 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.172717 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.172721 | 3 | 12 | 210 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.172737 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |