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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.
381,906 matroids, showing 18,601–18,650
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.352681 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.352730 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.352739 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.352750 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.352761 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.352782 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.352794 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.352826 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.352844 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.352855 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.352912 | 3 | 12 | 209 | 2 | ✓ | all | 6 | ? |
| 3.12.352923 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.352949 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.353019 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.353058 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.353061 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.353067 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.353081 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.353089 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.353107 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.353136 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.353140 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.353154 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.353181 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.353225 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.353248 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.353301 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.353319 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.353364 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.353378 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.353392 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.353396 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.353399 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.353441 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.353445 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.353565 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.353571 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.353587 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.353588 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.353590 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.353605 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.353611 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.353613 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.353645 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.353692 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.353724 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.353735 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.353746 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.353771 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.353778 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |