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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 18,951–19,000
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.363033 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.363102 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.363142 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.363208 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.363300 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.363305 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.363324 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.363359 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.363365 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.363379 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.363442 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.363478 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.363554 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.363607 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.363638 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.363681 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.363683 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.363700 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.363744 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.363770 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.363844 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.363987 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.363996 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.364009 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.364026 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.364033 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.364036 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.364051 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.364147 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.364201 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.364234 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.364270 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.364415 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.364426 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.364429 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.364431 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.364439 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.364444 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.364456 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.364464 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.364476 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.364501 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.364518 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.364519 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.364544 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.364551 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.364555 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.364563 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.364574 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.364593 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |