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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.
3,622,905 matroids, showing 19,301–19,350
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.73746 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73747 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73748 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73749 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73751 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73752 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73754 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73755 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73757 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.73758 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73759 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73760 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73761 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73762 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73763 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73768 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73771 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73772 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.73773 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73774 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73775 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73776 | 3 | 11 | 153 | 2 | ✓ | all | 4 | rational |
| 3.11.73777 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73783 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73789 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73790 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73793 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73794 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73795 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73796 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73797 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73798 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73804 | 3 | 11 | 154 | 1 | ✓ | all | 4 | rational |
| 3.11.73806 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73808 | 3 | 11 | 153 | 1 | ✓ | all | 4 | rational |
| 3.11.73814 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73824 | 3 | 11 | 152 | 2 | ✓ | all | 4 | rational |
| 3.11.73826 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73827 | 3 | 11 | 152 | 1 | ✓ | all | 4 | empty |
| 3.11.73828 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73831 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.73833 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.73836 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73841 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |
| 3.11.73843 | 3 | 11 | 150 | 1 | ✓ | all | 4 | rational |
| 3.11.73845 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73846 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73849 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73853 | 3 | 11 | 152 | 1 | ✓ | all | 4 | rational |
| 3.11.73855 | 3 | 11 | 151 | 1 | ✓ | all | 4 | rational |