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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 19,901–19,950
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.140826 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.140854 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.140855 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.140860 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.140881 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.140885 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.140889 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.140892 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,7,13 | 0 | ? |
| 3.12.140894 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.140909 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.140926 | 3 | 12 | 210 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.140958 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7,13,19 | 0 | ? |
| 3.12.140961 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.140962 | 3 | 12 | 209 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.140979 | 3 | 12 | 210 | 1 | ✓ | all but 7 | 0 | ? |
| 3.12.140983 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.140984 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.140991 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.140997 | 3 | 12 | 209 | 1 | ✓ | all but 2,11 | 0 | ? |
| 3.12.140998 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.141001 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.141023 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.141026 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.141040 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.141047 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.141053 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.141061 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.141069 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.141090 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.141093 | 3 | 12 | 209 | 1 | ✓ | all but 2,11 | 0 | ? |
| 3.12.141105 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.141106 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.141122 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.141123 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.141139 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.141152 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.141160 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.141191 | 3 | 12 | 210 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.141197 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.141198 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,11,13 | 0 | ? |
| 3.12.141199 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.141206 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.141215 | 3 | 12 | 210 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.141226 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.141247 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.141251 | 3 | 12 | 208 | 1 | ✓ | all but 2,5,11 | 0 | ? |
| 3.12.141254 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.141271 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7,13 | 0 | ? |
| 3.12.141276 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.141288 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |