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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.
32,400,859 matroids, showing 21,201–21,250
| label ▼ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 4.9.169013 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169012 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169011 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169010 | 4 | 9 | 107 | 1 | ✓ | all but 2,3,5 | 0 | rational |
| 4.9.169009 | 4 | 9 | 108 | 1 | ✓ | all | 1 | rational |
| 4.9.169008 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169007 | 4 | 9 | 108 | 1 | ✓ | all | 4 | rational |
| 4.9.169006 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |
| 4.9.169005 | 4 | 9 | 108 | 1 | ✓ | all but 2 | 2 | rational |
| 4.9.169004 | 4 | 9 | 109 | 1 | ✓ | all | 2 | rational |
| 4.9.169003 | 4 | 9 | 107 | 1 | ✓ | all but 2 | 2 | rational |
| 4.9.169002 | 4 | 9 | 108 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169001 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169000 | 4 | 9 | 108 | 1 | ✓ | all but 2 | 3 | rational |
| 4.9.168999 | 4 | 9 | 109 | 1 | ✓ | all but 2 | 2 | rational |
| 4.9.168998 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.168997 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.168996 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |
| 4.9.168995 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |
| 4.9.168994 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.168993 | 4 | 9 | 108 | 1 | ✓ | {5} | -1 | rational |
| 4.9.168992 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.168991 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |
| 4.9.168990 | 4 | 9 | 109 | 1 | ✓ | all but 2,5 | 0 | rational |
| 4.9.168989 | 4 | 9 | 107 | 1 | ✓ | all but 2,3,5,7 | 0 | rational |
| 4.9.168988 | 4 | 9 | 108 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.168987 | 4 | 9 | 108 | 1 | ✓ | all | 5 | rational |
| 4.9.168986 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.168985 | 4 | 9 | 109 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.168984 | 4 | 9 | 108 | 1 | ✓ | all | 4 | rational |
| 4.9.168983 | 4 | 9 | 109 | 1 | ✓ | all | 1 | rational |
| 4.9.168982 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.168981 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.168980 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.168979 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.168978 | 4 | 9 | 109 | 1 | ✓ | all | 3 | rational |
| 4.9.168977 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.168976 | 4 | 9 | 108 | 1 | ✓ | all | 1 | rational |
| 4.9.168975 | 4 | 9 | 109 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.168974 | 4 | 9 | 109 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.168973 | 4 | 9 | 109 | 1 | ✓ | all but 2 | 2 | rational |
| 4.9.168972 | 4 | 9 | 109 | 1 | ✓ | all | 3 | rational |
| 4.9.168971 | 4 | 9 | 110 | 1 | ✓ | all | 2 | rational |
| 4.9.168970 | 4 | 9 | 107 | 1 | ✓ | all | 5 | rational |
| 4.9.168969 | 4 | 9 | 107 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.168968 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.168967 | 4 | 9 | 108 | 1 | ✓ | all but 2,3 | 1 | rational |
| 4.9.168966 | 4 | 9 | 106 | 1 | ✓ | all but 2 | 1 | rational over Q(a)/(a^2 - a + 1) |
| 4.9.168965 | 4 | 9 | 106 | 1 | ✓ | all | 2 | rational |
| 4.9.168964 | 4 | 9 | 107 | 1 | ✓ | {3} | -1 | rational |