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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 18,801–18,850
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.357933 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.357991 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.358065 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.358153 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.358219 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.358231 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.358255 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.358267 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.358276 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.358286 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.358316 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.358442 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.358519 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.358546 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.358587 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.358667 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.358756 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.358788 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.358791 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.358810 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.358815 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.358821 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.358953 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.358985 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.359059 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.359176 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.359204 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.359810 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.359824 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.359842 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.359862 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.359903 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.359925 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.360062 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.360065 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.360072 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.360084 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.360097 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.360101 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.360164 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.360197 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.360198 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.360205 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.360227 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.360465 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.360469 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.360472 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.360481 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.360492 | 3 | 12 | 211 | 1 | ✓ | all | 6 | ? |
| 3.12.360493 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |