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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 18,451–18,500
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.348825 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.348828 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.348832 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.348835 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.348837 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.348838 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.348840 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.348846 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.348881 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.348930 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.349010 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.349035 | 3 | 12 | 211 | 1 | ✓ | all | 6 | ? |
| 3.12.349038 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.349052 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.349089 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.349220 | 3 | 12 | 211 | 1 | ✓ | all | 6 | ? |
| 3.12.349274 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.349287 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.349296 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.349298 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.349316 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.349327 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.349345 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.349396 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.349398 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.349422 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.349428 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.349437 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.349447 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.349448 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.349449 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.349471 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.349477 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.349480 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.349506 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.349521 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.349522 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.349564 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.349570 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.349622 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.349669 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.349671 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.349684 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.349688 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.349692 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.349697 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.350177 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.350181 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.350207 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.350217 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |