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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 22,401–22,450
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.174510 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.174515 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,7,11 | 0 | ? |
| 3.12.174533 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,7,11,13 | 0 | ? |
| 3.12.174535 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.174540 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.174551 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.174553 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.174565 | 3 | 12 | 207 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.174579 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.174580 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.174591 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.174607 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7,11,13,17 | 0 | ? |
| 3.12.174610 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.174611 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.174622 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7,11 | 0 | ? |
| 3.12.174625 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.174631 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.174642 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.174644 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.174660 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7,13 | 0 | ? |
| 3.12.174672 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.174684 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.174695 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.174717 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.174730 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.174735 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.174746 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.174752 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.174776 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,7,13,17 | 0 | ? |
| 3.12.174797 | 3 | 12 | 209 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.174807 | 3 | 12 | 207 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.174809 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,7,11,13 | 0 | ? |
| 3.12.174838 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,7,11,17 | 0 | ? |
| 3.12.174855 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.174862 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.174883 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.174885 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,7,13,17 | 0 | ? |
| 3.12.174891 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.174892 | 3 | 12 | 207 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.174914 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.174972 | 3 | 12 | 207 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.174978 | 3 | 12 | 207 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.175016 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.175022 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.175030 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.175034 | 3 | 12 | 207 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.175042 | 3 | 12 | 208 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.175044 | 3 | 12 | 208 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.175100 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.175123 | 3 | 12 | 208 | 2 | ✓ | all but 2,5 | 0 | ? |