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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 20,451–20,500
| label ▼ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 4.9.169763 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169762 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169761 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169760 | 4 | 9 | 106 | 1 | ✓ | all | 2 | rational |
| 4.9.169759 | 4 | 9 | 107 | 1 | ✓ | all but 2,5 | 0 | rational |
| 4.9.169758 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169757 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169756 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |
| 4.9.169755 | 4 | 9 | 106 | 1 | ✓ | all | 1 | rational |
| 4.9.169754 | 4 | 9 | 106 | 1 | ✓ | all | 1 | rational |
| 4.9.169753 | 4 | 9 | 106 | 1 | ✓ | all | 3 | rational |
| 4.9.169752 | 4 | 9 | 107 | 1 | ✓ | all | 0 | rational |
| 4.9.169751 | 4 | 9 | 106 | 1 | ✓ | all | 1 | rational |
| 4.9.169750 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169749 | 4 | 9 | 106 | 1 | ✓ | all | 1 | rational |
| 4.9.169748 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169747 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169746 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169745 | 4 | 9 | 108 | 1 | ✓ | all | 1 | rational |
| 4.9.169744 | 4 | 9 | 107 | 2 | ✓ | all | 2 | rational |
| 4.9.169743 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169742 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169741 | 4 | 9 | 108 | 1 | ✓ | all | 1 | rational |
| 4.9.169740 | 4 | 9 | 106 | 2 | ✓ | ∅ | -1 | rational |
| 4.9.169739 | 4 | 9 | 107 | 2 | ✓ | all | 4 | rational |
| 4.9.169738 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169737 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169736 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169735 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169734 | 4 | 9 | 108 | 2 | ✓ | all | 1 | rational |
| 4.9.169733 | 4 | 9 | 109 | 2 | ✓ | all | 3 | rational |
| 4.9.169732 | 4 | 9 | 105 | 1 | ✓ | all | 2 | rational |
| 4.9.169731 | 4 | 9 | 105 | 1 | ✓ | all | 3 | rational |
| 4.9.169730 | 4 | 9 | 106 | 1 | ✓ | all | 3 | rational |
| 4.9.169729 | 4 | 9 | 106 | 1 | ✓ | all | 1 | rational |
| 4.9.169728 | 4 | 9 | 105 | 1 | ✓ | all | 2 | rational |
| 4.9.169727 | 4 | 9 | 106 | 1 | ✓ | all | 2 | rational |
| 4.9.169726 | 4 | 9 | 106 | 1 | ✓ | all | 1 | rational |
| 4.9.169725 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169724 | 4 | 9 | 106 | 1 | ✓ | all | 3 | rational |
| 4.9.169723 | 4 | 9 | 106 | 1 | ✓ | all | 4 | rational |
| 4.9.169722 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169721 | 4 | 9 | 106 | 1 | ✓ | all | 2 | rational |
| 4.9.169720 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169719 | 4 | 9 | 105 | 1 | ✓ | all | 4 | point over Q(a)/(a^2 - a + 1) |
| 4.9.169718 | 4 | 9 | 106 | 1 | ✓ | all | 3 | rational |
| 4.9.169717 | 4 | 9 | 106 | 1 | ✓ | all | 2 | rational |
| 4.9.169716 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169715 | 4 | 9 | 106 | 1 | ✓ | all | 4 | rational |
| 4.9.169714 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |