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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 19,001–19,050
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.127075 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.127097 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.127125 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.127127 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.127130 | 3 | 12 | 208 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.127131 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.127132 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.127135 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.127169 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.127215 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.127235 | 3 | 12 | 210 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.127258 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.127292 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.127309 | 3 | 12 | 208 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.127335 | 3 | 12 | 212 | 2 | ✓ | all but 2,13 | 0 | ? |
| 3.12.127336 | 3 | 12 | 212 | 2 | ✓ | all but 2,3,5,13 | 0 | ? |
| 3.12.127338 | 3 | 12 | 212 | 2 | ✓ | all but 2 | 0 | ? |
| 3.12.127346 | 3 | 12 | 211 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.127368 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.127424 | 3 | 12 | 211 | 1 | ✓ | all | 0 | ? |
| 3.12.127440 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.127462 | 3 | 12 | 211 | 1 | ✓ | all | 0 | ? |
| 3.12.127489 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.127490 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.127607 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.127625 | 3 | 12 | 209 | 1 | ✓ | all but 2,11 | 0 | ? |
| 3.12.127629 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.127658 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.127666 | 3 | 12 | 211 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.127694 | 3 | 12 | 211 | 1 | ✓ | all but 7 | 0 | ? |
| 3.12.127738 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.127789 | 3 | 12 | 211 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.127793 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.127801 | 3 | 12 | 210 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.127822 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.127843 | 3 | 12 | 210 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.128166 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.128254 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.128274 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.128311 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.128320 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.128334 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.128336 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.128439 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.128452 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.128483 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.128504 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.128506 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.128522 | 3 | 12 | 211 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.128535 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |