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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 21,051–21,100
| label ▼ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 4.9.169163 | 4 | 9 | 109 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169162 | 4 | 9 | 108 | 1 | ✓ | all but 2 | 2 | rational |
| 4.9.169161 | 4 | 9 | 108 | 1 | ✓ | all but 2,3,5 | 0 | rational |
| 4.9.169160 | 4 | 9 | 109 | 1 | ✓ | all | 3 | rational |
| 4.9.169159 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169158 | 4 | 9 | 108 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169157 | 4 | 9 | 108 | 1 | ✓ | all but 2 | 2 | rational |
| 4.9.169156 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |
| 4.9.169155 | 4 | 9 | 109 | 1 | ✓ | all | 4 | rational |
| 4.9.169154 | 4 | 9 | 108 | 1 | ✓ | all | 1 | rational |
| 4.9.169153 | 4 | 9 | 108 | 1 | ✓ | all | 1 | rational |
| 4.9.169152 | 4 | 9 | 109 | 1 | ✓ | all | 2 | rational |
| 4.9.169151 | 4 | 9 | 108 | 1 | ✓ | all but 2,3,5 | 0 | rational |
| 4.9.169150 | 4 | 9 | 108 | 1 | ✓ | all but 2 | 2 | rational |
| 4.9.169149 | 4 | 9 | 109 | 1 | ✓ | all | 2 | rational |
| 4.9.169148 | 4 | 9 | 109 | 1 | ✓ | all but 2,3,5 | 0 | rational |
| 4.9.169147 | 4 | 9 | 109 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169146 | 4 | 9 | 109 | 1 | ✓ | all | 3 | rational |
| 4.9.169145 | 4 | 9 | 110 | 1 | ✓ | all | 1 | rational |
| 4.9.169144 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169143 | 4 | 9 | 108 | 1 | ✓ | all | 5 | rational |
| 4.9.169142 | 4 | 9 | 107 | 1 | ✓ | {2} | -1 | rational |
| 4.9.169141 | 4 | 9 | 107 | 1 | ✓ | all | 6 | rational |
| 4.9.169140 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169139 | 4 | 9 | 108 | 1 | ✓ | all but 2 | 3 | rational |
| 4.9.169138 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169137 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169136 | 4 | 9 | 107 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169135 | 4 | 9 | 106 | 1 | ✓ | all | 1 | rational |
| 4.9.169134 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169133 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169132 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169131 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169130 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169129 | 4 | 9 | 108 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169128 | 4 | 9 | 108 | 1 | ✓ | all but 2 | 2 | rational |
| 4.9.169127 | 4 | 9 | 109 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169126 | 4 | 9 | 106 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169125 | 4 | 9 | 107 | 1 | ✓ | all but 2,3,7 | 0 | rational |
| 4.9.169124 | 4 | 9 | 106 | 1 | ✓ | all but 2,3,5 | 0 | rational |
| 4.9.169123 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169122 | 4 | 9 | 106 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169121 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169120 | 4 | 9 | 107 | 1 | ✓ | all but 2 | 2 | rational |
| 4.9.169119 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169118 | 4 | 9 | 106 | 1 | ✓ | all | 1 | rational |
| 4.9.169117 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169116 | 4 | 9 | 107 | 1 | ✓ | all but 2 | 2 | rational |
| 4.9.169115 | 4 | 9 | 107 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169114 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |