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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 18,851–18,900
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.125627 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.125630 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,11 | 0 | ? |
| 3.12.125632 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.125649 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.125672 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.125687 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.125708 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.125711 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.125715 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.125721 | 3 | 12 | 209 | 1 | ✓ | all but 2,29 | 0 | ? |
| 3.12.125725 | 3 | 12 | 208 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.125727 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.125734 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.125743 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.125745 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.125751 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.125763 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,7 | 0 | ? |
| 3.12.125794 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.125800 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.125806 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.125807 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.125821 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.125826 | 3 | 12 | 208 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.125827 | 3 | 12 | 208 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.125836 | 3 | 12 | 209 | 1 | ✓ | all but 3 | 0 | ? |
| 3.12.125839 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.125840 | 3 | 12 | 212 | 2 | ✓ | all but 2 | 0 | ? |
| 3.12.125859 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.125868 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5,7 | 0 | ? |
| 3.12.125879 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5,7,11,19 | 0 | ? |
| 3.12.125885 | 3 | 12 | 210 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.125890 | 3 | 12 | 209 | 1 | ✓ | all but 2,7 | 0 | ? |
| 3.12.125898 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5,11 | 0 | ? |
| 3.12.125899 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.125902 | 3 | 12 | 210 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.125915 | 3 | 12 | 209 | 1 | ✓ | all but 2 | 0 | ? |
| 3.12.125919 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.125934 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5,13 | 0 | ? |
| 3.12.125938 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.125945 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.125951 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,5,7,13 | 0 | ? |
| 3.12.125953 | 3 | 12 | 209 | 1 | ✓ | all | 0 | ? |
| 3.12.125959 | 3 | 12 | 209 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.125966 | 3 | 12 | 210 | 1 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.126011 | 3 | 12 | 208 | 2 | ✓ | all but 2,3,5 | 0 | ? |
| 3.12.126014 | 3 | 12 | 209 | 1 | ✓ | all but 2,3,11 | 0 | ? |
| 3.12.126018 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |
| 3.12.126020 | 3 | 12 | 209 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.126028 | 3 | 12 | 208 | 1 | ✓ | all but 2,5 | 0 | ? |
| 3.12.126029 | 3 | 12 | 208 | 1 | ✓ | all but 2,3 | 0 | ? |