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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 19,451–19,500
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.135454 | 3 | 12 | 210 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.135455 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.135464 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.135471 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.135476 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.135479 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.135499 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.135500 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.135512 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.135518 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.135540 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.135590 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.135602 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.135603 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.135620 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.135634 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.135640 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.135650 | 3 | 12 | 211 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.135663 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.135675 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.135676 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.135683 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,7,17 | 0 | ? |
| 3.12.135690 | 3 | 12 | 210 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.135693 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.135694 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.135723 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.135733 | 3 | 12 | 209 | 1 | ✓ | all but 2,7,13 | 0 | ? |
| 3.12.135734 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.135737 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.135738 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.135741 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.135753 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.135754 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.135763 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.135777 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.135780 | 3 | 12 | 210 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.135785 | 3 | 12 | 212 | 1 | ✓ | all | 0 | ? |
| 3.12.135816 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.135819 | 3 | 12 | 210 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.135837 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.135865 | 3 | 12 | 210 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.135873 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.135891 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.135894 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.135899 | 3 | 12 | 210 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.135942 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.135961 | 3 | 12 | 209 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.135962 | 3 | 12 | 211 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.135981 | 3 | 12 | 210 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.135994 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |