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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 18,701–18,750
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.123322 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.123334 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.123349 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.123357 | 3 | 12 | 208 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.123360 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.123380 | 3 | 12 | 210 | 1 | ✓ | all but 5 | 0 | ? |
| 3.12.123463 | 3 | 12 | 210 | 1 | ✓ | all but 5,11 | 0 | ? |
| 3.12.123514 | 3 | 12 | 211 | 1 | ✓ | all but 5 | 0 | ? |
| 3.12.123550 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.123559 | 3 | 12 | 211 | 1 | ✓ | all but 5 | 0 | ? |
| 3.12.123569 | 3 | 12 | 210 | 1 | ✓ | all but 5 | 0 | ? |
| 3.12.123580 | 3 | 12 | 211 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.123597 | 3 | 12 | 210 | 1 | ✓ | all but 5 | 0 | ? |
| 3.12.123614 | 3 | 12 | 210 | 1 | ✓ | all but 5 | 0 | ? |
| 3.12.123650 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.123698 | 3 | 12 | 210 | 1 | ✓ | all | 0 | ? |
| 3.12.123725 | 3 | 12 | 210 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.123727 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.123733 | 3 | 12 | 209 | 1 | ✓ | all but 2,11 | 0 | ? |
| 3.12.123744 | 3 | 12 | 209 | 1 | ✓ | all but 5 | 0 | ? |
| 3.12.123748 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.123759 | 3 | 12 | 210 | 1 | ✓ | all but 5 | 0 | ? |
| 3.12.123848 | 3 | 12 | 210 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.123859 | 3 | 12 | 210 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.123867 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.123923 | 3 | 12 | 210 | 1 | ✓ | all but 5 | 0 | ? |
| 3.12.123925 | 3 | 12 | 210 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.123971 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.123986 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.124015 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.124029 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.124033 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.124035 | 3 | 12 | 211 | 1 | ✓ | all | 0 | ? |
| 3.12.124047 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.124061 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.124063 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,7,11 | 0 | ? |
| 3.12.124076 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.124084 | 3 | 12 | 208 | 1 | ✓ | all | 0 | ? |
| 3.12.124122 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.124124 | 3 | 12 | 208 | 1 | ✓ | all but 5 | 0 | ? |
| 3.12.124126 | 3 | 12 | 208 | 1 | ✓ | all but 2,11 | 0 | ? |
| 3.12.124128 | 3 | 12 | 208 | 1 | ✓ | all but 5 | 0 | ? |
| 3.12.124137 | 3 | 12 | 209 | 1 | ✓ | all but 5 | 0 | ? |
| 3.12.124153 | 3 | 12 | 208 | 1 | ✓ | all but 5 | 0 | ? |
| 3.12.124163 | 3 | 12 | 210 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.124219 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.124227 | 3 | 12 | 210 | 1 | ✓ | all but 5 | 0 | ? |
| 3.12.124230 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.124242 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.124262 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |