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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 21,251–21,300
| label ▼ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 4.9.168963 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.168962 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.168961 | 4 | 9 | 107 | 1 | ✓ | all but 2 | 2 | rational |
| 4.9.168960 | 4 | 9 | 107 | 1 | ✓ | all | 6 | rational |
| 4.9.168959 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.168958 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.168957 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.168956 | 4 | 9 | 107 | 1 | ✓ | all | 0 | rational |
| 4.9.168955 | 4 | 9 | 108 | 1 | ✓ | all but 2,3 | 2 | rational |
| 4.9.168954 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.168953 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.168952 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.168951 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |
| 4.9.168950 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.168949 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.168948 | 4 | 9 | 108 | 1 | ✓ | all | 1 | rational |
| 4.9.168947 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |
| 4.9.168946 | 4 | 9 | 109 | 1 | ✓ | all | 5 | rational |
| 4.9.168945 | 4 | 9 | 107 | 1 | ✓ | all but 2,3 | 1 | rational |
| 4.9.168944 | 4 | 9 | 107 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.168943 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.168942 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.168941 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.168940 | 4 | 9 | 108 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.168939 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.168938 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.168937 | 4 | 9 | 109 | 1 | ✓ | all | 3 | rational |
| 4.9.168936 | 4 | 9 | 107 | 1 | ✓ | all but 2 | 2 | rational |
| 4.9.168935 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.168934 | 4 | 9 | 108 | 1 | ✓ | all | 1 | rational |
| 4.9.168933 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |
| 4.9.168932 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.168931 | 4 | 9 | 108 | 1 | ✓ | all but 2,3,5 | 0 | rational |
| 4.9.168930 | 4 | 9 | 108 | 1 | ✓ | all but 2,3,5 | 0 | rational |
| 4.9.168929 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.168928 | 4 | 9 | 109 | 1 | ✓ | all | 1 | rational |
| 4.9.168927 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.168926 | 4 | 9 | 108 | 1 | ✓ | all | 1 | rational |
| 4.9.168925 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.168924 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |
| 4.9.168923 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.168922 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.168921 | 4 | 9 | 109 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.168920 | 4 | 9 | 108 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.168919 | 4 | 9 | 108 | 1 | ✓ | all | 6 | rational |
| 4.9.168918 | 4 | 9 | 109 | 1 | ✓ | all | 1 | rational |
| 4.9.168917 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.168916 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.168915 | 4 | 9 | 109 | 1 | ✓ | all | 1 | rational |
| 4.9.168914 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |