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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 22,251–22,300
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.442484 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.442508 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.442532 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.442561 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.442599 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.442615 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.442624 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.442633 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.442646 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.442655 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.442660 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.442677 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.442683 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.442701 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.442702 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.442728 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.442767 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.442773 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.442783 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.442791 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.442821 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.442823 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.442843 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.442857 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.442866 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.442933 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.442945 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.442955 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.442958 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.442985 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.443098 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.443114 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.443117 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.443152 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.443167 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.443171 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.443186 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.443217 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.443237 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.443271 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.443312 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.443321 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.443333 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.443343 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.443347 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.443349 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.443350 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.443352 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.443355 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.443360 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |