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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 22,001–22,050
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.437798 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.437799 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.437807 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.437826 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.437841 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.437854 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.437857 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.437863 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.437873 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.437878 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.437900 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.437905 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.437922 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.437943 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.437965 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.438033 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.438043 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.438093 | 3 | 12 | 210 | 2 | ✓ | all | 6 | ? |
| 3.12.438100 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.438116 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.438122 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.438264 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.438272 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.438284 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.438292 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.438295 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.438303 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.438324 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.438373 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.438376 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.438398 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.438411 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.438445 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.438456 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.438475 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.438492 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.438500 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.438502 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.438541 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.438579 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.438658 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.438666 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.438704 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.438718 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.438751 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.438782 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.438823 | 3 | 12 | 210 | 1 | ✓ | all | 6 | ? |
| 3.12.438832 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.438891 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.439011 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |