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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.
2,030,492 matroids, showing 22,751–22,800
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.180241 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.180247 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.180251 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.180253 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.180264 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.180274 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.180275 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.180277 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.180280 | 3 | 12 | 207 | 1 | ✓ | all | 0 | ? |
| 3.12.180315 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.180321 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.180328 | 3 | 12 | 211 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.180342 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.180370 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.180381 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,13 | 0 | ? |
| 3.12.180397 | 3 | 12 | 210 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.180420 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.180437 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.180445 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.180448 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.180453 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.180454 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.180458 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.180468 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.180475 | 3 | 12 | 209 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.180551 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.180553 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.180557 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.180577 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.180591 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.180594 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.180632 | 3 | 12 | 208 | 1 | ✓ | all but 7 | 0 | ? |
| 3.12.180653 | 3 | 12 | 208 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.180658 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.180705 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.180719 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.180723 | 3 | 12 | 207 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.180730 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.180749 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.180762 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.180774 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.180778 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.180796 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.180797 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.180801 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.180817 | 3 | 12 | 208 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.180853 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.180861 | 3 | 12 | 211 | 2 | ✓ | all but 2,3 | 0 | ? |
| 3.12.180874 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.180886 | 3 | 12 | 210 | 1 | ✓ | all but 3 | 0 | ? |