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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 20,601–20,650
| label ▼ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 4.9.169613 | 4 | 9 | 108 | 2 | ✓ | all | 1 | rational |
| 4.9.169612 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169611 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169610 | 4 | 9 | 109 | 1 | ✓ | all but 2,3 | 0 | rational |
| 4.9.169609 | 4 | 9 | 109 | 1 | ✓ | all | 3 | rational |
| 4.9.169608 | 4 | 9 | 109 | 2 | ✓ | all | 4 | rational |
| 4.9.169607 | 4 | 9 | 110 | 2 | ✓ | all | 3 | rational |
| 4.9.169606 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169605 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169604 | 4 | 9 | 106 | 1 | ✓ | all | 4 | rational |
| 4.9.169603 | 4 | 9 | 107 | 1 | ✓ | all but 2,5 | 0 | rational |
| 4.9.169602 | 4 | 9 | 105 | 1 | ✓ | all | 1 | empty |
| 4.9.169601 | 4 | 9 | 106 | 1 | ✓ | all | 3 | rational |
| 4.9.169600 | 4 | 9 | 106 | 1 | ✓ | all | 3 | rational |
| 4.9.169599 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169598 | 4 | 9 | 106 | 1 | ✓ | all | 4 | rational |
| 4.9.169597 | 4 | 9 | 106 | 1 | ✓ | all | 4 | rational |
| 4.9.169596 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169595 | 4 | 9 | 107 | 1 | ✓ | all but 2,3,5,7 | 0 | rational |
| 4.9.169594 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169593 | 4 | 9 | 108 | 1 | ✓ | all | 1 | rational |
| 4.9.169592 | 4 | 9 | 106 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169591 | 4 | 9 | 106 | 1 | ✓ | all | 3 | rational |
| 4.9.169590 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169589 | 4 | 9 | 106 | 1 | ✓ | all | 3 | rational |
| 4.9.169588 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169587 | 4 | 9 | 105 | 1 | ✓ | ∅ | -1 | point over Q(a)/(a^2 + 1) |
| 4.9.169586 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169585 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169584 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169583 | 4 | 9 | 106 | 1 | ✓ | all | 2 | rational |
| 4.9.169582 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169581 | 4 | 9 | 107 | 1 | ✓ | all | 5 | rational |
| 4.9.169580 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169579 | 4 | 9 | 105 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169578 | 4 | 9 | 105 | 1 | ✓ | all | 3 | rational |
| 4.9.169577 | 4 | 9 | 106 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169576 | 4 | 9 | 106 | 1 | ✓ | all | 2 | rational |
| 4.9.169575 | 4 | 9 | 105 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169574 | 4 | 9 | 106 | 1 | ✓ | all | 4 | rational |
| 4.9.169573 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169572 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169571 | 4 | 9 | 106 | 1 | ✓ | all but 2,3,5,7 | 0 | rational |
| 4.9.169570 | 4 | 9 | 106 | 1 | ✓ | all | 1 | rational |
| 4.9.169569 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169568 | 4 | 9 | 106 | 1 | ✓ | all | 2 | rational |
| 4.9.169567 | 4 | 9 | 106 | 1 | ✓ | all | 3 | rational |
| 4.9.169566 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169565 | 4 | 9 | 106 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169564 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |