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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 21,601–21,650
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.427647 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.427713 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.427764 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.427768 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.427780 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.427799 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.427814 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.427816 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.427921 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.427966 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.427991 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.428009 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.428035 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.428040 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.428078 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.428098 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.428101 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.428181 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.428266 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.428269 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.428308 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.428314 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.428322 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.428332 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.428337 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.428358 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.428381 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.428387 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.428391 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.428404 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.428465 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.428470 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.428616 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.428640 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.428649 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.428681 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.428695 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.428775 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.428784 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.428825 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.428830 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.428835 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.428855 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.428861 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.428895 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.428909 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.428919 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.428942 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.429099 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.429101 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |