Search
…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 20,501–20,550
| label ▼ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 4.9.169713 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169712 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169711 | 4 | 9 | 106 | 2 | ✓ | all | 3 | rational |
| 4.9.169710 | 4 | 9 | 106 | 1 | ✓ | all | 1 | rational |
| 4.9.169709 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169708 | 4 | 9 | 106 | 1 | ✓ | all | 4 | rational |
| 4.9.169707 | 4 | 9 | 107 | 1 | ✓ | all but 2,3 | 0 | rational |
| 4.9.169706 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169705 | 4 | 9 | 106 | 1 | ✓ | all | 2 | rational |
| 4.9.169704 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169703 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169702 | 4 | 9 | 108 | 1 | ✓ | all | 4 | rational |
| 4.9.169701 | 4 | 9 | 105 | 2 | ✓ | all | 2 | point over Q(a)/(a^2 - a + 1) |
| 4.9.169700 | 4 | 9 | 106 | 2 | ✓ | ∅ | -1 | rational |
| 4.9.169699 | 4 | 9 | 106 | 1 | ✓ | all | 3 | rational |
| 4.9.169698 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169697 | 4 | 9 | 106 | 1 | ✓ | all | 1 | rational |
| 4.9.169696 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169695 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169694 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169693 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169692 | 4 | 9 | 106 | 1 | ✓ | all | 4 | rational |
| 4.9.169691 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169690 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169689 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |
| 4.9.169688 | 4 | 9 | 107 | 2 | ✓ | all | 3 | rational |
| 4.9.169687 | 4 | 9 | 108 | 2 | ✓ | all | 4 | rational |
| 4.9.169686 | 4 | 9 | 106 | 1 | ✓ | all | 3 | rational |
| 4.9.169685 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169684 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169683 | 4 | 9 | 108 | 1 | ✓ | all | 1 | rational |
| 4.9.169682 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169681 | 4 | 9 | 108 | 1 | ✓ | all but 2,7 | 0 | rational |
| 4.9.169680 | 4 | 9 | 106 | 1 | ✓ | all | 2 | rational |
| 4.9.169679 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169678 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169677 | 4 | 9 | 108 | 1 | ✓ | all | 4 | rational |
| 4.9.169676 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169675 | 4 | 9 | 107 | 1 | ✓ | all | 0 | rational |
| 4.9.169674 | 4 | 9 | 108 | 1 | ✓ | all but 3 | 0 | rational |
| 4.9.169673 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169672 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169671 | 4 | 9 | 109 | 1 | ✓ | all | 2 | rational |
| 4.9.169670 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169669 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169668 | 4 | 9 | 106 | 1 | ✓ | all but 2,5 | 0 | rational |
| 4.9.169667 | 4 | 9 | 106 | 1 | ✓ | all | 2 | rational |
| 4.9.169666 | 4 | 9 | 107 | 1 | ✓ | all | 5 | rational |
| 4.9.169665 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169664 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |