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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 19,351–19,400
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.371471 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.371479 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.371507 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.371515 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.371564 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.371610 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.371795 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.371913 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.371949 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.372064 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.372194 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.372300 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.372319 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.372357 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.372404 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.372407 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.372440 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.372442 | 3 | 12 | 209 | 2 | ✓ | all | 6 | ? |
| 3.12.372443 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.372458 | 3 | 12 | 206 | 2 | ✓ | all | 6 | ? |
| 3.12.372466 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.372507 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.372521 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.372523 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.372531 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.372557 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.372559 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.372577 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.372582 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.372586 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.372589 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.372604 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.372617 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.372668 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.372685 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.372690 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.372714 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.372724 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.372732 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.372766 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.372773 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.372852 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.372876 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.372894 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.372913 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.372947 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.372948 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.372984 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.372997 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.373001 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |