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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 20,901–20,950
| label ▼ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 4.9.169313 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169312 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169311 | 4 | 9 | 108 | 1 | ✓ | all | 0 | rational |
| 4.9.169310 | 4 | 9 | 108 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169309 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169308 | 4 | 9 | 109 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169307 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169306 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169305 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169304 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169303 | 4 | 9 | 109 | 1 | ✓ | all but 2 | 0 | rational |
| 4.9.169302 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169301 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169300 | 4 | 9 | 109 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169299 | 4 | 9 | 108 | 1 | ✓ | all | 1 | rational |
| 4.9.169298 | 4 | 9 | 109 | 1 | ✓ | all | 1 | rational |
| 4.9.169297 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169296 | 4 | 9 | 108 | 1 | ✓ | all | 1 | rational |
| 4.9.169295 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169294 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169293 | 4 | 9 | 109 | 1 | ✓ | all | 3 | rational |
| 4.9.169292 | 4 | 9 | 108 | 1 | ✓ | all | 5 | rational |
| 4.9.169291 | 4 | 9 | 108 | 1 | ✓ | all but 2,5 | 0 | rational |
| 4.9.169290 | 4 | 9 | 109 | 1 | ✓ | all | 1 | rational |
| 4.9.169289 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169288 | 4 | 9 | 108 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169287 | 4 | 9 | 109 | 1 | ✓ | all | 1 | rational |
| 4.9.169286 | 4 | 9 | 109 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169285 | 4 | 9 | 109 | 1 | ✓ | {2} | -1 | rational |
| 4.9.169284 | 4 | 9 | 109 | 1 | ✓ | all | 3 | rational |
| 4.9.169283 | 4 | 9 | 110 | 1 | ✓ | all | 1 | rational |
| 4.9.169282 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169281 | 4 | 9 | 107 | 1 | ✓ | all | 5 | rational |
| 4.9.169280 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | empty |
| 4.9.169279 | 4 | 9 | 106 | 1 | ✓ | all | 2 | rational |
| 4.9.169278 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169277 | 4 | 9 | 107 | 1 | ✓ | all but 2,3,5 | 0 | rational |
| 4.9.169276 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169275 | 4 | 9 | 108 | 1 | ✓ | all but 2,3,5,7 | 0 | rational |
| 4.9.169274 | 4 | 9 | 106 | 1 | ✓ | all | 3 | rational |
| 4.9.169273 | 4 | 9 | 106 | 1 | ✓ | all | 1 | rational |
| 4.9.169272 | 4 | 9 | 107 | 1 | ✓ | all but 2,5 | 0 | rational |
| 4.9.169271 | 4 | 9 | 106 | 1 | ✓ | all but 2,3,5,7 | 0 | rational |
| 4.9.169270 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169269 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169268 | 4 | 9 | 106 | 1 | ✓ | all | 2 | rational |
| 4.9.169267 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169266 | 4 | 9 | 106 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169265 | 4 | 9 | 107 | 1 | ✓ | all but 2 | 0 | rational |
| 4.9.169264 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |