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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.
2,030,492 matroids, showing 22,351–22,400
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.173920 | 3 | 12 | 208 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.173926 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.173928 | 3 | 12 | 209 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.173949 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.173950 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.173963 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.173983 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.174000 | 3 | 12 | 209 | 1 | ✓ | all but 2,5,11 | 0 | ? |
| 3.12.174002 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.174006 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.174030 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.174036 | 3 | 12 | 208 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.174039 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.174044 | 3 | 12 | 209 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.174081 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.174083 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.174094 | 3 | 12 | 207 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.174096 | 3 | 12 | 207 | 1 | ✓ | all but 2,3,13 | 0 | ? |
| 3.12.174099 | 3 | 12 | 207 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.174106 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.174108 | 3 | 12 | 207 | 2 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.174111 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,11 | 0 | ? |
| 3.12.174142 | 3 | 12 | 207 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.174146 | 3 | 12 | 207 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.174179 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.174187 | 3 | 12 | 207 | 1 | ✓ | all | 0 | ? |
| 3.12.174191 | 3 | 12 | 207 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.174208 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,13 | 0 | ? |
| 3.12.174222 | 3 | 12 | 208 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.174242 | 3 | 12 | 207 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.174283 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.174289 | 3 | 12 | 207 | 1 | ✓ | all | 0 | ? |
| 3.12.174316 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.174321 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.174323 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.174330 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.174331 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.174336 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.174337 | 3 | 12 | 207 | 1 | ✓ | all but 5 | 0 | ? |
| 3.12.174343 | 3 | 12 | 207 | 1 | ✓ | all but 2,3,5,11 | 0 | ? |
| 3.12.174348 | 3 | 12 | 207 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.174381 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.174405 | 3 | 12 | 208 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.174416 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.174417 | 3 | 12 | 207 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.174441 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.174447 | 3 | 12 | 207 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.174470 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5,7,13 | 0 | ? |
| 3.12.174491 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.174495 | 3 | 12 | 207 | 1 | ✓ | all but 5 | 0 | ? |