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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 22,551–22,600
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.449445 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.449455 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.449471 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.449485 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.449495 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.449534 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.449592 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.449653 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.449689 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.449780 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.449833 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.449882 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.449927 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.449928 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.449939 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.449946 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.449949 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.449962 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.449967 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.449969 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.449988 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.450038 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.450044 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.450070 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.450074 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.450128 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.450148 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.450226 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.450234 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.450256 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.450271 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.450294 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.450304 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.450309 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.450313 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.450339 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.450349 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.450364 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.450379 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.450380 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.450456 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.450474 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.450504 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.450534 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.450566 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.450569 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.450572 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.450577 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.450579 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.450604 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |