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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 21,701–21,750
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.430234 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.430304 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.430317 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.430330 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.430368 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.430380 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.430398 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.430407 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.430411 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.430422 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.430468 | 3 | 12 | 207 | 2 | ✓ | all | 6 | ? |
| 3.12.430473 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.430518 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.430537 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.430559 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.430594 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.430596 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.430597 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.430613 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.430624 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.430642 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.430673 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.430687 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.430710 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.430712 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.430755 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.430794 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.430850 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.430854 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.430883 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.430895 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.430924 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.430933 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.430940 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.430959 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.430973 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.430983 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.431004 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.431112 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.431130 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.431146 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.431151 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.431168 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.431177 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.431207 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.431297 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.431309 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.431390 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.431445 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.431532 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |