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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 22,451–22,500
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.175123 | 3 | 12 | 208 | 2 | ✓ | all but 2,5 | 0 | ? |
| 3.12.175135 | 3 | 12 | 210 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.175142 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.175162 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7,11 | 0 | ? |
| 3.12.175164 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.175244 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.175265 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.175276 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,11 | 0 | ? |
| 3.12.175281 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,11 | 0 | ? |
| 3.12.175305 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.175324 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.175328 | 3 | 12 | 208 | 1 | ✓ | all but 5 | 0 | ? |
| 3.12.175405 | 3 | 12 | 208 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.175424 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.175435 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.175453 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.175468 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.175478 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,11 | 0 | ? |
| 3.12.175480 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.175488 | 3 | 12 | 209 | 1 | ✓ | all but 5 | 0 | ? |
| 3.12.175509 | 3 | 12 | 208 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.175536 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,17 | 0 | ? |
| 3.12.175550 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.175576 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,7,11 | 0 | ? |
| 3.12.175662 | 3 | 12 | 207 | 1 | ✓ | all but 2,3,7,11 | 0 | ? |
| 3.12.175711 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.175757 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,7,23 | 0 | ? |
| 3.12.175790 | 3 | 12 | 210 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.175793 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.176192 | 3 | 12 | 208 | 2 | ✓ | all | 0 | ? |
| 3.12.176225 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.176227 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.176241 | 3 | 12 | 207 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.176249 | 3 | 12 | 209 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.176367 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.176385 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.176405 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.176416 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.176417 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.176421 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.176460 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.176550 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.176561 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.176676 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.176681 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.176697 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.176735 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.176743 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.176747 | 3 | 12 | 209 | 1 | ✓ | all but 5 | 0 | ? |
| 3.12.176782 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |