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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 20,751–20,800
| label ▼ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 4.9.169463 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169462 | 4 | 9 | 106 | 1 | ✓ | all | 3 | rational |
| 4.9.169461 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169460 | 4 | 9 | 106 | 1 | ✓ | all | 4 | rational |
| 4.9.169459 | 4 | 9 | 107 | 1 | ✓ | all but 2,3 | 0 | rational |
| 4.9.169458 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169457 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169456 | 4 | 9 | 106 | 1 | ✓ | all | 1 | rational |
| 4.9.169455 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169454 | 4 | 9 | 107 | 1 | ✓ | all but 2,3,5 | 0 | rational |
| 4.9.169453 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |
| 4.9.169452 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169451 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |
| 4.9.169450 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169449 | 4 | 9 | 108 | 1 | ✓ | all | 1 | rational |
| 4.9.169448 | 4 | 9 | 106 | 1 | ✓ | all | 3 | rational |
| 4.9.169447 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169446 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169445 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169444 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169443 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169442 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169441 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169440 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169439 | 4 | 9 | 108 | 1 | ✓ | all | 4 | rational |
| 4.9.169438 | 4 | 9 | 108 | 1 | ✓ | all but 2,3 | 1 | rational |
| 4.9.169437 | 4 | 9 | 109 | 1 | ✓ | all | 2 | rational |
| 4.9.169436 | 4 | 9 | 106 | 1 | ✓ | all | 1 | rational |
| 4.9.169435 | 4 | 9 | 105 | 1 | ✓ | ∅ | -1 | point over Q(a)/(a^2 - a - 1) |
| 4.9.169434 | 4 | 9 | 106 | 1 | ✓ | all | 3 | rational |
| 4.9.169433 | 4 | 9 | 106 | 1 | ✓ | all | 3 | rational |
| 4.9.169432 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169431 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169430 | 4 | 9 | 106 | 1 | ✓ | all but 2 | 0 | rational |
| 4.9.169429 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169428 | 4 | 9 | 106 | 1 | ✓ | all | 1 | rational |
| 4.9.169427 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169426 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169425 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169424 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169423 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |
| 4.9.169422 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169421 | 4 | 9 | 106 | 1 | ✓ | all | 2 | rational |
| 4.9.169420 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169419 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169418 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169417 | 4 | 9 | 107 | 1 | ✓ | all but 2,3,5,7 | 0 | rational |
| 4.9.169416 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169415 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169414 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |