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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 22,501–22,550
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.448579 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.448582 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.448605 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.448612 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.448618 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.448642 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.448648 | 3 | 12 | 205 | 2 | ✓ | all | 6 | ? |
| 3.12.448659 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.448694 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.448754 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.448765 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.448773 | 3 | 12 | 206 | 2 | ✓ | all | 6 | ? |
| 3.12.448780 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.448788 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.448796 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.448804 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.448812 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.448837 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.448845 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.448851 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.448853 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.448912 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.448971 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.449019 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.449025 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.449032 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.449051 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.449067 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.449068 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.449079 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.449092 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.449157 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.449168 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.449270 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.449330 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.449350 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.449362 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.449366 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.449368 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.449382 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.449383 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.449385 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.449386 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.449396 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.449397 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.449402 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.449414 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.449417 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.449422 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.449426 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |