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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 22,301–22,350
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.443365 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.443366 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.443382 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.443383 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.443416 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.443427 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.443433 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.443435 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.443500 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.443517 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.443543 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.443593 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.443634 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.443663 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.443675 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.443793 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.443802 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.443857 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.443945 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.443961 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.443967 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.443969 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.443989 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.444009 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.444016 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.444017 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.444026 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.444041 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.444057 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.444082 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.444095 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.444114 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.444180 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.444237 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.444245 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.444260 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.444274 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.444301 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.444359 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.444378 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.444381 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.444397 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.444400 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.444402 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.444403 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.444412 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.444416 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.444417 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.444426 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.444430 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |