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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 19,451–19,500
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.374353 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.374356 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.374371 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.374389 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.374392 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.374401 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.374515 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.374516 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.374518 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.374527 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.374557 | 3 | 12 | 209 | 2 | ✓ | all | 6 | ? |
| 3.12.374563 | 3 | 12 | 211 | 4 | ✓ | all | 6 | ? |
| 3.12.374582 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.374583 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.374637 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.374676 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.374679 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.374684 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.374695 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.374835 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.374841 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.374852 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.374864 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.374875 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.374967 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.374987 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.374991 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.374996 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.374998 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.375003 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.375013 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.375053 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.375054 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.375055 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.375056 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.375088 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.375094 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.375104 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.375105 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.375115 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.375119 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.375120 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.375122 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.375126 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.375128 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.375151 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.375174 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.375179 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.375180 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.375185 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |