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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 19,001–19,050
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.364626 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.364639 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.364647 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.364696 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.364711 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.364714 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.364819 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.364829 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.364891 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.364908 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.364935 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.364962 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.364980 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.364981 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.364982 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.365066 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.365098 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.365120 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.365141 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.365149 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.365184 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.365197 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.365198 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.365214 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.365236 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.365278 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.365307 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.365337 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.365345 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.365365 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.365378 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.365384 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.365424 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.365493 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.365503 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.365520 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.365542 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.365562 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.365571 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.365625 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.365633 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.365686 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.365709 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.365732 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.365760 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.365870 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.365884 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.365885 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.365902 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.365938 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |