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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 19,751–19,800
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.139454 | 3 | 12 | 208 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.139458 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.139465 | 3 | 12 | 209 | 2 | ✓ | all but 2 | 0 | ? |
| 3.12.139472 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.139494 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.139495 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.139498 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.139503 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.139510 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.139521 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.139559 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5,7,11,13,23 | 0 | ? |
| 3.12.139560 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.139562 | 3 | 12 | 211 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.139574 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5,19 | 0 | ? |
| 3.12.139580 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.139591 | 3 | 12 | 211 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.139596 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.139598 | 3 | 12 | 211 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.139615 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.139616 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.139620 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.139621 | 3 | 12 | 209 | 1 | ✓ | all but 7 | 0 | ? |
| 3.12.139630 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.139672 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.139674 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.139679 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.139694 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.139695 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.139696 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7,11 | 0 | ? |
| 3.12.139701 | 3 | 12 | 209 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.139715 | 3 | 12 | 208 | 1 | ✓ | all but 2,11 | 0 | ? |
| 3.12.139721 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.139725 | 3 | 12 | 208 | 2 | ✓ | all but 2 | 0 | ? |
| 3.12.139749 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.139753 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.139762 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.139770 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.139803 | 3 | 12 | 210 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.139812 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.139831 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.139834 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.139835 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.139842 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.139845 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.139848 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.139881 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.139884 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.139895 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.139896 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.139899 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |