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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 20,351–20,400
| label ▼ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 4.9.169863 | 4 | 9 | 106 | 1 | ✓ | all | 1 | rational |
| 4.9.169862 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169861 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169860 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169859 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169858 | 4 | 9 | 107 | 2 | ✓ | all | 2 | rational |
| 4.9.169857 | 4 | 9 | 106 | 1 | ✓ | all | 2 | rational |
| 4.9.169856 | 4 | 9 | 106 | 1 | ✓ | all | 1 | rational |
| 4.9.169855 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169854 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169853 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169852 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169851 | 4 | 9 | 106 | 1 | ✓ | all | 4 | empty |
| 4.9.169850 | 4 | 9 | 106 | 1 | ✓ | all | 2 | rational |
| 4.9.169849 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169848 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169847 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169846 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169845 | 4 | 9 | 107 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169844 | 4 | 9 | 108 | 1 | ✓ | all | 1 | rational |
| 4.9.169843 | 4 | 9 | 106 | 2 | ✓ | all | 3 | empty |
| 4.9.169842 | 4 | 9 | 107 | 2 | ✓ | ∅ | -1 | empty |
| 4.9.169841 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169840 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169839 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169838 | 4 | 9 | 108 | 1 | ✓ | all | 4 | rational |
| 4.9.169837 | 4 | 9 | 108 | 2 | ✓ | all | 3 | rational |
| 4.9.169836 | 4 | 9 | 109 | 2 | ✓ | all | 5 | rational |
| 4.9.169835 | 4 | 9 | 103 | 2 | ✓ | all | 2 | rational |
| 4.9.169834 | 4 | 9 | 104 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169833 | 4 | 9 | 104 | 2 | ✓ | all | 3 | rational |
| 4.9.169832 | 4 | 9 | 105 | 2 | ✓ | ∅ | -1 | rational |
| 4.9.169831 | 4 | 9 | 103 | 1 | ✓ | all | 1 | rational |
| 4.9.169830 | 4 | 9 | 104 | 1 | ✓ | all | 1 | rational |
| 4.9.169829 | 4 | 9 | 104 | 1 | ✓ | all | 4 | rational |
| 4.9.169828 | 4 | 9 | 105 | 1 | ✓ | all | 3 | rational |
| 4.9.169827 | 4 | 9 | 104 | 1 | ✓ | all | 3 | rational |
| 4.9.169826 | 4 | 9 | 105 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169825 | 4 | 9 | 104 | 1 | ✓ | all | 3 | rational |
| 4.9.169824 | 4 | 9 | 105 | 1 | ✓ | all | 2 | rational |
| 4.9.169823 | 4 | 9 | 104 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169822 | 4 | 9 | 105 | 1 | ✓ | all | 2 | rational |
| 4.9.169821 | 4 | 9 | 105 | 1 | ✓ | all | 1 | rational |
| 4.9.169820 | 4 | 9 | 106 | 1 | ✓ | all | 1 | rational |
| 4.9.169819 | 4 | 9 | 104 | 1 | ✓ | all | 4 | empty |
| 4.9.169818 | 4 | 9 | 104 | 1 | ✓ | all | 2 | empty |
| 4.9.169817 | 4 | 9 | 105 | 1 | ✓ | all | 2 | empty |
| 4.9.169816 | 4 | 9 | 105 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169815 | 4 | 9 | 105 | 1 | ✓ | ∅ | -1 | empty |
| 4.9.169814 | 4 | 9 | 106 | 1 | ✓ | all | 2 | rational |