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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.
4,238,885 matroids, showing 21,551–21,600
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.12.19767 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.19772 | 3 | 12 | 209 | 1 | ✓ | {11} | -1 | ? |
| 3.12.19796 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.19806 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.19812 | 3 | 12 | 210 | 1 | ✓ | {2} | -1 | ? |
| 3.12.19818 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.19829 | 3 | 12 | 210 | 1 | ✓ | {11} | -1 | ? |
| 3.12.19830 | 3 | 12 | 210 | 1 | ✓ | {19} | -1 | ? |
| 3.12.19835 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.19845 | 3 | 12 | 209 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.19848 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.19850 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.19859 | 3 | 12 | 211 | 1 | ✓ | {3} | -1 | ? |
| 3.12.19871 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.19879 | 3 | 12 | 209 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.19892 | 3 | 12 | 209 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.19893 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.19903 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.19912 | 3 | 12 | 209 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.19918 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.19919 | 3 | 12 | 212 | 1 | ✓ | {23} | -1 | ? |
| 3.12.19923 | 3 | 12 | 212 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.19928 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.19929 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.19942 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.19946 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.19957 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.19961 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.19962 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.19981 | 3 | 12 | 210 | 1 | ✓ | {79} | -1 | ? |
| 3.12.19985 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.19991 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.19994 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.19996 | 3 | 12 | 212 | 2 | ✓ | ∅ | -1 | ? |
| 3.12.20001 | 3 | 12 | 210 | 1 | ✓ | {29} | -1 | ? |
| 3.12.20002 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.20008 | 3 | 12 | 211 | 2 | ✓ | {41} | -1 | ? |
| 3.12.20013 | 3 | 12 | 211 | 1 | ✓ | {11} | -1 | ? |
| 3.12.20023 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.20024 | 3 | 12 | 211 | 2 | ✓ | ∅ | -1 | ? |
| 3.12.20026 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.20028 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.20030 | 3 | 12 | 209 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.20031 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.20034 | 3 | 12 | 211 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.20037 | 3 | 12 | 210 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.20041 | 3 | 12 | 209 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.20042 | 3 | 12 | 209 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.20045 | 3 | 12 | 209 | 1 | ✓ | ∅ | -1 | ? |
| 3.12.20051 | 3 | 12 | 211 | 2 | ✓ | ∅ | -1 | ? |