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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 22,201–22,250
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.441669 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.441696 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.441710 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.441714 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.441807 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.441837 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.441852 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.441856 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.441859 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.441873 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.441889 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.441895 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.441911 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.441932 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.441934 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.441940 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.441947 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.441952 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.441958 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.441960 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.441974 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.441981 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.441984 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.441998 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.442006 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.442014 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.442023 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.442035 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.442050 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.442060 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.442076 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.442087 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.442092 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.442115 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.442140 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.442154 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.442171 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.442187 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.442213 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.442214 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.442225 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.442251 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.442262 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.442268 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.442317 | 3 | 12 | 206 | 1 | ✓ | all | 6 | ? |
| 3.12.442343 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.442346 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.442350 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.442362 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.442364 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |