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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.
5,849,183 matroids, showing 22,351–22,400
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.185756 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.185757 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.185759 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.185760 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.185792 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.185793 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.185794 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.185796 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.185797 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.185798 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.185807 | 3 | 11 | 148 | 1 | ✓ | all but 2 | 1 | genus 1 curve (14a4) |
| 3.11.185808 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.185809 | 3 | 11 | 147 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.185812 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.185813 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.185821 | 3 | 11 | 149 | 2 | ✓ | all | 1 | rational |
| 3.11.185822 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.185823 | 3 | 11 | 147 | 2 | ✓ | all | 1 | rational |
| 3.11.185825 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.185826 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.185827 | 3 | 11 | 147 | 2 | ✓ | all but 2 | 1 | rational |
| 3.11.185829 | 3 | 11 | 146 | 2 | ✓ | all | 1 | rational over Q(a)/(a^2 - a + 1) |
| 3.11.185830 | 3 | 11 | 148 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.185831 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.185832 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.185864 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.185865 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.185866 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.185869 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.185870 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.185871 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.185877 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.185878 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.185879 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.185881 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.185882 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.185890 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.185891 | 3 | 11 | 148 | 1 | ✓ | all | 1 | genus 1 curve (11a3) |
| 3.11.185892 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.185895 | 3 | 11 | 148 | 1 | ✓ | all | 1 | genus 1 curve (11a3) |
| 3.11.185896 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.185897 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.185899 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational over Q(a)/(a^2 - a + 1) |
| 3.11.185900 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.185901 | 3 | 11 | 146 | 1 | ✓ | all | 1 | rational |
| 3.11.185934 | 3 | 11 | 147 | 1 | ✓ | all | 1 | point over Q(a)/(a^4 - a^3 + 2*a - 1) |
| 3.11.185935 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.185936 | 3 | 11 | 147 | 1 | ✓ | all | 1 | point over Q(a)/(a^3 - a^2 + 1) |
| 3.11.185938 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.185939 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |