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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 21,001–21,050
| label ▼ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 4.9.169213 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169212 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169211 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169210 | 4 | 9 | 107 | 1 | ✓ | all | 1 | empty |
| 4.9.169209 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169208 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169207 | 4 | 9 | 108 | 1 | ✓ | all but 2,3 | 0 | rational |
| 4.9.169206 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169205 | 4 | 9 | 108 | 1 | ✓ | all | 4 | rational |
| 4.9.169204 | 4 | 9 | 108 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169203 | 4 | 9 | 109 | 1 | ✓ | all but 2,3,5 | 0 | rational |
| 4.9.169202 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169201 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169200 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169199 | 4 | 9 | 106 | 1 | ✓ | all | 2 | rational |
| 4.9.169198 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169197 | 4 | 9 | 107 | 1 | ✓ | all but 2 | 2 | rational |
| 4.9.169196 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169195 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169194 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169193 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169192 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169191 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |
| 4.9.169190 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169189 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |
| 4.9.169188 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169187 | 4 | 9 | 107 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169186 | 4 | 9 | 108 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169185 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169184 | 4 | 9 | 108 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169183 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169182 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169181 | 4 | 9 | 108 | 1 | ✓ | all but 2 | 2 | rational |
| 4.9.169180 | 4 | 9 | 108 | 1 | ✓ | all | 5 | rational |
| 4.9.169179 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169178 | 4 | 9 | 109 | 1 | ✓ | all | 1 | rational |
| 4.9.169177 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169176 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169175 | 4 | 9 | 108 | 1 | ✓ | all but 2 | 2 | rational |
| 4.9.169174 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169173 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169172 | 4 | 9 | 108 | 1 | ✓ | all | 1 | rational |
| 4.9.169171 | 4 | 9 | 108 | 1 | ✓ | {2} | -1 | rational |
| 4.9.169170 | 4 | 9 | 109 | 1 | ✓ | all | 1 | rational |
| 4.9.169169 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169168 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |
| 4.9.169167 | 4 | 9 | 108 | 1 | ✓ | all | 1 | rational |
| 4.9.169166 | 4 | 9 | 108 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169165 | 4 | 9 | 109 | 1 | ✓ | all | 1 | rational |
| 4.9.169164 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |