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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 19,051–19,100
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.365949 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.365955 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.365986 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.365997 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.366007 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.366025 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.366123 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.366218 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.366257 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.366260 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.366262 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.366289 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.366298 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.366353 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.366446 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.366479 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.366566 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.366603 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.366656 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.366661 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.366670 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.366687 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.366756 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.366803 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.366808 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.366814 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.366819 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.366835 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.366836 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.366847 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.366853 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.366854 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.366867 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.366869 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.366887 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.366922 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.366979 | 3 | 12 | 208 | 2 | ✓ | all | 6 | ? |
| 3.12.366996 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367003 | 3 | 12 | 209 | 1 | ✓ | all | 6 | ? |
| 3.12.367007 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367019 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367034 | 3 | 12 | 207 | 1 | ✓ | all | 6 | ? |
| 3.12.367042 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367051 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367207 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367220 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367229 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367234 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367236 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |
| 3.12.367238 | 3 | 12 | 208 | 1 | ✓ | all | 6 | ? |