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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 21,901–21,950
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.434244 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.434254 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.434273 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.434335 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.434401 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.434500 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.434620 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.434627 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.434633 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.434641 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.434670 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.434682 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.434693 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.434707 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.434719 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.434721 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.434760 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.434810 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.435003 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.435014 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.435018 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.435030 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.435031 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.435033 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.435053 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.435078 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.435092 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.435199 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.435230 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.435285 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.435344 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.435398 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.435454 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.435469 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.435485 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.435495 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.435501 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.435507 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.435529 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.435548 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.435571 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.435704 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.435736 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.435891 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.436065 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.436069 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.436080 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.436087 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.436119 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.436138 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |