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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 18,401–18,450
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.346810 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.346811 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.346841 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.346851 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.346864 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.346945 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.346948 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.346966 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.347033 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.347075 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.347076 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.347127 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.347134 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.347171 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.347351 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.347496 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.347604 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.347655 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.347855 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.347861 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.347891 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.347907 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.347950 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.347970 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.347988 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.347994 | 3 | 12 | 211 | 1 | ✓ | all | 6 | ? |
| 3.12.348001 | 3 | 12 | 210 | 2 | ✓ | all | 6 | ? |
| 3.12.348097 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.348230 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.348256 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.348376 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.348380 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.348501 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.348512 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.348513 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.348534 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.348544 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.348560 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.348590 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.348608 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.348611 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.348617 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.348690 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.348714 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.348723 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.348744 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.348774 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.348797 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.348808 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.348822 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |