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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 22,501–22,550
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.176908 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.176930 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.176963 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.176968 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,13 | 0 | ? |
| 3.12.177055 | 3 | 12 | 208 | 2 | ✓ | all but 2 | 0 | ? |
| 3.12.177069 | 3 | 12 | 207 | 1 | ✓ | all | 0 | ? |
| 3.12.177080 | 3 | 12 | 207 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.177082 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.177089 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.177115 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.177121 | 3 | 12 | 208 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.177123 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.177131 | 3 | 12 | 207 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.177173 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.177270 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.177272 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.177274 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.177323 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.177444 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.177458 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.177468 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.177556 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.177596 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.177608 | 3 | 12 | 208 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.177635 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.177638 | 3 | 12 | 211 | 2 | ✓ | all | 0 | ? |
| 3.12.177660 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.177725 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.177807 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.177812 | 3 | 12 | 208 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.177814 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.177815 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.177839 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.177840 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.177841 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.177856 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.177860 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.177873 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.177934 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.177957 | 3 | 12 | 208 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.177959 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.177965 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.177971 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.177985 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.177999 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.178002 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.178005 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.178008 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.178013 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.178015 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |