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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 18,851–18,900
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.360494 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.360502 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.360505 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.360620 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.360625 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.360631 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.360646 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.360650 | 3 | 12 | 211 | 1 | ✓ | all | 6 | ? |
| 3.12.360738 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.360818 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.360827 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.360838 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.360858 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.360868 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.360887 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.360896 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.360920 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.360932 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.360982 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.360985 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.360992 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.360999 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.361087 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.361166 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.361172 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.361185 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.361195 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.361197 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.361222 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.361257 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.361262 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.361328 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.361349 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.361558 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.361560 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.361572 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.361596 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.361597 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.361601 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.361613 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.361628 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.361640 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.361642 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.361692 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.361698 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.361745 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.361755 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.361778 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.361805 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.361838 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |