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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 18,501–18,550
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.350251 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.350379 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.350389 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.350411 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.350422 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.350429 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.350645 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.350659 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.350663 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.350694 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.350702 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.350705 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.350754 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.350784 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.350811 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.350824 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.350835 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.350947 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.351016 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.351025 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.351029 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.351036 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.351055 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.351057 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.351075 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.351086 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.351101 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.351115 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.351145 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.351162 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.351165 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.351333 | 3 | 12 | 208 | 2 | ✓ | all | 6 | ? |
| 3.12.351340 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.351342 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.351351 | 3 | 12 | 208 | 2 | ✓ | all | 6 | ? |
| 3.12.351355 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.351363 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.351374 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.351376 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.351379 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.351384 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.351399 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.351419 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.351420 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.351428 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.351443 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.351464 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.351470 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.351486 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.351531 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |