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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 21,151–21,200
| label ▼ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 4.9.169063 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |
| 4.9.169062 | 4 | 9 | 108 | 1 | ✓ | all | 1 | rational |
| 4.9.169061 | 4 | 9 | 108 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169060 | 4 | 9 | 109 | 1 | ✓ | all | 2 | rational |
| 4.9.169059 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169058 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169057 | 4 | 9 | 109 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169056 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169055 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169054 | 4 | 9 | 109 | 1 | ✓ | all but 2 | 2 | rational |
| 4.9.169053 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169052 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |
| 4.9.169051 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169050 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169049 | 4 | 9 | 108 | 1 | ✓ | all | 5 | rational |
| 4.9.169048 | 4 | 9 | 108 | 1 | ✓ | all | 4 | rational |
| 4.9.169047 | 4 | 9 | 109 | 1 | ✓ | all | 4 | rational |
| 4.9.169046 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169045 | 4 | 9 | 108 | 1 | ✓ | all but 2 | 2 | rational |
| 4.9.169044 | 4 | 9 | 109 | 1 | ✓ | all but 2,5 | 0 | rational |
| 4.9.169043 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169042 | 4 | 9 | 108 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169041 | 4 | 9 | 109 | 1 | ✓ | all | 3 | rational |
| 4.9.169040 | 4 | 9 | 109 | 1 | ✓ | all | 2 | rational |
| 4.9.169039 | 4 | 9 | 109 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169038 | 4 | 9 | 109 | 1 | ✓ | all | 3 | rational |
| 4.9.169037 | 4 | 9 | 110 | 1 | ✓ | all but 2,3,5 | 0 | rational |
| 4.9.169036 | 4 | 9 | 104 | 2 | ✓ | all but 2 | 1 | rational |
| 4.9.169035 | 4 | 9 | 105 | 4 | ✓ | all | 5 | rational |
| 4.9.169034 | 4 | 9 | 105 | 2 | ✓ | all | 2 | rational |
| 4.9.169033 | 4 | 9 | 105 | 1 | ✓ | all but 2 | 3 | rational |
| 4.9.169032 | 4 | 9 | 106 | 2 | ✓ | all | 2 | rational |
| 4.9.169031 | 4 | 9 | 106 | 2 | ✓ | all | 1 | rational |
| 4.9.169030 | 4 | 9 | 105 | 2 | ✓ | ∅ | -1 | rational |
| 4.9.169029 | 4 | 9 | 106 | 4 | ✓ | all but 2 | 1 | rational |
| 4.9.169028 | 4 | 9 | 106 | 2 | ✓ | all | 1 | rational |
| 4.9.169027 | 4 | 9 | 107 | 4 | ✓ | all | 1 | rational |
| 4.9.169026 | 4 | 9 | 106 | 1 | ✓ | all but 2 | 2 | rational |
| 4.9.169025 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169024 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169023 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |
| 4.9.169022 | 4 | 9 | 106 | 1 | ✓ | all | 1 | rational |
| 4.9.169021 | 4 | 9 | 106 | 1 | ✓ | all | 6 | rational |
| 4.9.169020 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169019 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169018 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169017 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169016 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |
| 4.9.169015 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169014 | 4 | 9 | 107 | 1 | ✓ | all | 5 | rational |