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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 20,551–20,600
| label ▼ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 4.9.169663 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |
| 4.9.169662 | 4 | 9 | 107 | 2 | ✓ | all | 3 | empty |
| 4.9.169661 | 4 | 9 | 108 | 2 | ✓ | all | 1 | rational |
| 4.9.169660 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169659 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169658 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |
| 4.9.169657 | 4 | 9 | 108 | 1 | ✓ | all but 3 | 1 | rational |
| 4.9.169656 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169655 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169654 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169653 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169652 | 4 | 9 | 108 | 1 | ✓ | all | 4 | rational |
| 4.9.169651 | 4 | 9 | 108 | 1 | ✓ | all but 2,3,5,7 | 0 | rational |
| 4.9.169650 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169649 | 4 | 9 | 109 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169648 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169647 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169646 | 4 | 9 | 106 | 1 | ✓ | all | 2 | rational |
| 4.9.169645 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169644 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169643 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169642 | 4 | 9 | 108 | 1 | ✓ | all | 1 | rational |
| 4.9.169641 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169640 | 4 | 9 | 108 | 1 | ✓ | all | 1 | rational |
| 4.9.169639 | 4 | 9 | 106 | 1 | ✓ | all | 2 | rational |
| 4.9.169638 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169637 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169636 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169635 | 4 | 9 | 108 | 1 | ✓ | all but 3 | 0 | rational |
| 4.9.169634 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169633 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |
| 4.9.169632 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |
| 4.9.169631 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169630 | 4 | 9 | 109 | 1 | ✓ | all | 5 | rational |
| 4.9.169629 | 4 | 9 | 108 | 2 | ✓ | all | 2 | rational |
| 4.9.169628 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169627 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169626 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169625 | 4 | 9 | 108 | 1 | ✓ | all | 1 | rational |
| 4.9.169624 | 4 | 9 | 108 | 1 | ✓ | {2} | -1 | rational |
| 4.9.169623 | 4 | 9 | 109 | 1 | ✓ | all | 3 | rational |
| 4.9.169622 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169621 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169620 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169619 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169618 | 4 | 9 | 108 | 1 | ✓ | all | 1 | rational |
| 4.9.169617 | 4 | 9 | 108 | 1 | ✓ | {2} | -1 | rational |
| 4.9.169616 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169615 | 4 | 9 | 109 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169614 | 4 | 9 | 107 | 2 | ✓ | ∅ | -1 | rational |