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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 22,401–22,450
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.446508 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.446513 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.446551 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.446597 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.446607 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.446653 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.446682 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.446712 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.446719 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.446732 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.446737 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.446766 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.446785 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.446794 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.446823 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.446825 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.446836 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.446841 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.446892 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.446893 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.446922 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.446929 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.446934 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.446942 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.447055 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.447059 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.447078 | 3 | 12 | 210 | 2 | ✓ | all | 6 | ? |
| 3.12.447093 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.447111 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.447113 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.447170 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.447232 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.447276 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.447277 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.447281 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.447289 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.447299 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.447329 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.447339 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.447347 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.447353 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.447359 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.447363 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.447372 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.447376 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.447386 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.447390 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.447391 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.447428 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.447472 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |