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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 22,301–22,350
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.173347 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.173355 | 3 | 12 | 208 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.173359 | 3 | 12 | 210 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.173364 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.173367 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.173368 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.173369 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.173388 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.173390 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.173396 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.173399 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.173454 | 3 | 12 | 207 | 1 | ✓ | all but 2,3,7,11 | 0 | ? |
| 3.12.173469 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.173474 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.173477 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.173480 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.173490 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.173501 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.173509 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.173519 | 3 | 12 | 207 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.173570 | 3 | 12 | 207 | 1 | ✓ | all but 5,11 | 0 | ? |
| 3.12.173577 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.173614 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.173619 | 3 | 12 | 207 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.173631 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.173639 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,11 | 0 | ? |
| 3.12.173649 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.173663 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.173682 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.173705 | 3 | 12 | 207 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.173710 | 3 | 12 | 208 | 1 | ✓ | all but 2,5,11 | 0 | ? |
| 3.12.173716 | 3 | 12 | 208 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.173728 | 3 | 12 | 209 | 1 | ✓ | all but 2,11 | 0 | ? |
| 3.12.173733 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.173734 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.173735 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,11 | 0 | ? |
| 3.12.173736 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.173737 | 3 | 12 | 209 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.173754 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.173761 | 3 | 12 | 208 | 1 | ✓ | all but 2,5,11 | 0 | ? |
| 3.12.173774 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.173786 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.173794 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.173802 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.173845 | 3 | 12 | 209 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.173848 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.173864 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7,17 | 0 | ? |
| 3.12.173873 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.173891 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.173910 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,7,17 | 0 | ? |