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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 20,801–20,850
| label ▼ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 4.9.169413 | 4 | 9 | 108 | 1 | ✓ | all | 1 | rational |
| 4.9.169412 | 4 | 9 | 106 | 1 | ✓ | all | 5 | rational |
| 4.9.169411 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169410 | 4 | 9 | 107 | 1 | ✓ | all but 2,3,7 | 0 | rational |
| 4.9.169409 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169408 | 4 | 9 | 108 | 1 | ✓ | all | 5 | rational |
| 4.9.169407 | 4 | 9 | 107 | 1 | ✓ | {2} | -1 | rational |
| 4.9.169406 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169405 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169404 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169403 | 4 | 9 | 108 | 1 | ✓ | all | 4 | rational |
| 4.9.169402 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169401 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |
| 4.9.169400 | 4 | 9 | 109 | 1 | ✓ | all but 2,5 | 0 | rational |
| 4.9.169399 | 4 | 9 | 106 | 1 | ✓ | all | 3 | rational |
| 4.9.169398 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169397 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169396 | 4 | 9 | 106 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169395 | 4 | 9 | 107 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169394 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169393 | 4 | 9 | 108 | 1 | ✓ | all | 1 | rational |
| 4.9.169392 | 4 | 9 | 106 | 1 | ✓ | all | 2 | rational |
| 4.9.169391 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169390 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169389 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169388 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169387 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169386 | 4 | 9 | 106 | 1 | ✓ | all | 0 | rational |
| 4.9.169385 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169384 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169383 | 4 | 9 | 108 | 1 | ✓ | all but 2 | 2 | rational |
| 4.9.169382 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169381 | 4 | 9 | 108 | 1 | ✓ | all | 4 | rational |
| 4.9.169380 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169379 | 4 | 9 | 108 | 1 | ✓ | all | 4 | rational |
| 4.9.169378 | 4 | 9 | 108 | 1 | ✓ | all but 2 | 0 | rational |
| 4.9.169377 | 4 | 9 | 109 | 1 | ✓ | {2} | -1 | rational |
| 4.9.169376 | 4 | 9 | 105 | 1 | ✓ | all | 4 | point over Q(a)/(a^2 - a + 1) |
| 4.9.169375 | 4 | 9 | 106 | 1 | ✓ | all | 5 | rational |
| 4.9.169374 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169373 | 4 | 9 | 105 | 1 | ✓ | all | 4 | rational |
| 4.9.169372 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169371 | 4 | 9 | 106 | 1 | ✓ | all | 5 | rational |
| 4.9.169370 | 4 | 9 | 107 | 1 | ✓ | {2} | -1 | rational |
| 4.9.169369 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169368 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169367 | 4 | 9 | 107 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169366 | 4 | 9 | 106 | 1 | ✓ | all | 2 | rational |
| 4.9.169365 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169364 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | rational |