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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 20,401–20,450
| label ▼ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 4.9.169813 | 4 | 9 | 105 | 1 | ✓ | {5} | -1 | empty |
| 4.9.169812 | 4 | 9 | 105 | 1 | ✓ | all but 2 | 1 | empty |
| 4.9.169811 | 4 | 9 | 106 | 1 | ✓ | all | 2 | empty |
| 4.9.169810 | 4 | 9 | 105 | 1 | ✓ | all | 3 | point over Q(a)/(a^2 - a - 1) |
| 4.9.169809 | 4 | 9 | 106 | 1 | ✓ | all | 2 | rational |
| 4.9.169808 | 4 | 9 | 105 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169807 | 4 | 9 | 106 | 1 | ✓ | all | 2 | rational |
| 4.9.169806 | 4 | 9 | 106 | 1 | ✓ | all | 4 | rational |
| 4.9.169805 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169804 | 4 | 9 | 105 | 2 | ✓ | all | 2 | empty |
| 4.9.169803 | 4 | 9 | 105 | 1 | ✓ | ∅ | -1 | empty |
| 4.9.169802 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | empty |
| 4.9.169801 | 4 | 9 | 105 | 1 | ✓ | all | 2 | empty |
| 4.9.169800 | 4 | 9 | 106 | 1 | ✓ | all | 2 | rational |
| 4.9.169799 | 4 | 9 | 106 | 1 | ✓ | all | 1 | rational |
| 4.9.169798 | 4 | 9 | 106 | 1 | ✓ | all | 3 | empty |
| 4.9.169797 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169796 | 4 | 9 | 104 | 2 | ✓ | all | 3 | empty |
| 4.9.169795 | 4 | 9 | 105 | 2 | ✓ | all | 2 | empty |
| 4.9.169794 | 4 | 9 | 105 | 1 | ✓ | ∅ | -1 | empty |
| 4.9.169793 | 4 | 9 | 106 | 1 | ✓ | all | 3 | empty |
| 4.9.169792 | 4 | 9 | 105 | 1 | ✓ | all | 1 | rational |
| 4.9.169791 | 4 | 9 | 106 | 1 | ✓ | all | 1 | rational |
| 4.9.169790 | 4 | 9 | 106 | 1 | ✓ | all | 3 | rational |
| 4.9.169789 | 4 | 9 | 105 | 1 | ✓ | all but 2,3 | 0 | rational |
| 4.9.169788 | 4 | 9 | 106 | 1 | ✓ | all but 2,3,5 | 0 | rational |
| 4.9.169787 | 4 | 9 | 106 | 1 | ✓ | all but 2,5 | 0 | rational |
| 4.9.169786 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169785 | 4 | 9 | 106 | 2 | ✓ | all | 3 | empty |
| 4.9.169784 | 4 | 9 | 107 | 2 | ✓ | all | 1 | empty |
| 4.9.169783 | 4 | 9 | 105 | 1 | ✓ | all | 3 | rational |
| 4.9.169782 | 4 | 9 | 106 | 1 | ✓ | all | 3 | rational |
| 4.9.169781 | 4 | 9 | 106 | 1 | ✓ | all | 1 | rational |
| 4.9.169780 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169779 | 4 | 9 | 106 | 1 | ✓ | all | 2 | rational |
| 4.9.169778 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169777 | 4 | 9 | 106 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169776 | 4 | 9 | 106 | 1 | ✓ | all | 1 | rational |
| 4.9.169775 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169774 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169773 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169772 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |
| 4.9.169771 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169770 | 4 | 9 | 106 | 1 | ✓ | all | 2 | rational |
| 4.9.169769 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | rational over Q(a)/(a^2 - a - 1) |
| 4.9.169768 | 4 | 9 | 106 | 1 | ✓ | all but 2,5 | 0 | rational |
| 4.9.169767 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169766 | 4 | 9 | 106 | 2 | ✓ | all | 2 | empty |
| 4.9.169765 | 4 | 9 | 107 | 2 | ✓ | all | 4 | rational |
| 4.9.169764 | 4 | 9 | 106 | 1 | ✓ | all | 2 | rational |