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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 22,451–22,500
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.447484 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.447513 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.447524 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.447603 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.447606 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.447658 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.447698 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.447747 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.447827 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.447837 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.447842 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.447844 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.447856 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.447866 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.447869 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.447919 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.447979 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.448050 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.448088 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.448205 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.448210 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.448223 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.448230 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.448274 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.448305 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.448359 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.448361 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.448367 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.448370 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.448380 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.448383 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.448410 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.448413 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.448421 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.448425 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.448431 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.448447 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.448464 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.448481 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.448482 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.448487 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.448500 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.448502 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.448511 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.448518 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.448521 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.448531 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.448533 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.448534 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.448556 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |