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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 19,601–19,650
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.137587 | 3 | 12 | 207 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.137595 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.137612 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.137623 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.137642 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.137657 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.137667 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.137718 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.137721 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.137736 | 3 | 12 | 210 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.137745 | 3 | 12 | 209 | 1 | ✓ | all but 5 | 0 | ? |
| 3.12.137751 | 3 | 12 | 209 | 1 | ✓ | all but 2,11 | 0 | ? |
| 3.12.137764 | 3 | 12 | 209 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.137776 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.137778 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.137804 | 3 | 12 | 208 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.137818 | 3 | 12 | 211 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.137832 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7,11,13,19 | 0 | ? |
| 3.12.137833 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7,13 | 0 | ? |
| 3.12.137844 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.137870 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.137878 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.137890 | 3 | 12 | 208 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.137902 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.137929 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.137932 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.137943 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.137945 | 3 | 12 | 209 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.137949 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.137951 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.137983 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.137997 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.138011 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.138024 | 3 | 12 | 207 | 1 | ✓ | all | 0 | ? |
| 3.12.138037 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.138039 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.138041 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.138047 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7,11 | 0 | ? |
| 3.12.138063 | 3 | 12 | 207 | 1 | ✓ | all | 0 | ? |
| 3.12.138069 | 3 | 12 | 211 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.138077 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.138083 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.138090 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.138096 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.138121 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.138134 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.138136 | 3 | 12 | 210 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.138144 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.138159 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.138164 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |