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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 21,101–21,150
| label ▼ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 4.9.169113 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169112 | 4 | 9 | 107 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169111 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169110 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169109 | 4 | 9 | 107 | 1 | ✓ | all but 2,3 | 0 | rational |
| 4.9.169108 | 4 | 9 | 107 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169107 | 4 | 9 | 107 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169106 | 4 | 9 | 108 | 1 | ✓ | all | 4 | rational |
| 4.9.169105 | 4 | 9 | 107 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169104 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169103 | 4 | 9 | 108 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169102 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169101 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169100 | 4 | 9 | 108 | 1 | ✓ | all | 1 | rational |
| 4.9.169099 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169098 | 4 | 9 | 108 | 1 | ✓ | all but 2,3,5 | 0 | rational |
| 4.9.169097 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169096 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |
| 4.9.169095 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169094 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169093 | 4 | 9 | 109 | 1 | ✓ | all | 4 | rational |
| 4.9.169092 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169091 | 4 | 9 | 107 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169090 | 4 | 9 | 108 | 1 | ✓ | all | 5 | rational |
| 4.9.169089 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169088 | 4 | 9 | 106 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169087 | 4 | 9 | 107 | 1 | ✓ | all but 2,3,5,7 | 0 | rational |
| 4.9.169086 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169085 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169084 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169083 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169082 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169081 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169080 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169079 | 4 | 9 | 107 | 1 | ✓ | all | 5 | rational |
| 4.9.169078 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169077 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169076 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169075 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169074 | 4 | 9 | 108 | 1 | ✓ | all | 1 | rational |
| 4.9.169073 | 4 | 9 | 108 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169072 | 4 | 9 | 109 | 1 | ✓ | all | 4 | rational |
| 4.9.169071 | 4 | 9 | 108 | 1 | ✓ | all | 1 | rational |
| 4.9.169070 | 4 | 9 | 107 | 1 | ✓ | all but 2,3 | 1 | rational |
| 4.9.169069 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |
| 4.9.169068 | 4 | 9 | 108 | 1 | ✓ | all | 1 | rational |
| 4.9.169067 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169066 | 4 | 9 | 109 | 1 | ✓ | all | 3 | rational |
| 4.9.169065 | 4 | 9 | 108 | 1 | ✓ | all | 4 | rational |
| 4.9.169064 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |