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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 20,851–20,900
| label ▼ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 4.9.169363 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169362 | 4 | 9 | 107 | 1 | ✓ | all | 5 | rational |
| 4.9.169361 | 4 | 9 | 108 | 1 | ✓ | all | 5 | rational |
| 4.9.169360 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169359 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169358 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169357 | 4 | 9 | 106 | 1 | ✓ | all | 2 | rational |
| 4.9.169356 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169355 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169354 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169353 | 4 | 9 | 106 | 1 | ✓ | all | 4 | rational |
| 4.9.169352 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169351 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169350 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169349 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169348 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169347 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169346 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169345 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169344 | 4 | 9 | 108 | 1 | ✓ | all | 5 | rational |
| 4.9.169343 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169342 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169341 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169340 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169339 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169338 | 4 | 9 | 108 | 1 | ✓ | all | 1 | rational |
| 4.9.169337 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169336 | 4 | 9 | 109 | 1 | ✓ | all | 1 | rational |
| 4.9.169335 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169334 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169333 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169332 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169331 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169330 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169329 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169328 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169327 | 4 | 9 | 107 | 1 | ✓ | all but 2,5 | 0 | rational |
| 4.9.169326 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169325 | 4 | 9 | 108 | 1 | ✓ | all | 4 | rational |
| 4.9.169324 | 4 | 9 | 107 | 1 | ✓ | all but 2 | 2 | rational |
| 4.9.169323 | 4 | 9 | 108 | 1 | ✓ | all | 6 | rational |
| 4.9.169322 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169321 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169320 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169319 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169318 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169317 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169316 | 4 | 9 | 109 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169315 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169314 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |