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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 21,751–21,800
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.431550 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.431644 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.431674 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.431675 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.431676 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.431695 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.431758 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.431792 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.431825 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.431909 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.431950 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.431969 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.431972 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.432006 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.432024 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.432040 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.432048 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.432055 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.432074 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.432078 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.432089 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.432212 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.432233 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.432256 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.432262 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.432290 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.432314 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.432328 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.432338 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.432376 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.432406 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.432407 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.432410 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.432427 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.432449 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.432452 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.432508 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.432638 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.432649 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.432683 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.432723 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.432737 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.432743 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.432764 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.432765 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.432817 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.432834 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.432864 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.432968 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.433006 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |