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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 22,601–22,650
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.186655 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186658 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186661 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186663 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186665 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186671 | 3 | 11 | 147 | 1 | ✓ | all | 1 | rational |
| 3.11.186672 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186779 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186781 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186783 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186784 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186813 | 3 | 11 | 148 | 1 | ✓ | all | 1 | genus 1 curve (37a1) |
| 3.11.186814 | 3 | 11 | 148 | 1 | ✓ | all | 1 | genus 1 curve (11a3) |
| 3.11.186816 | 3 | 11 | 146 | 1 | ✓ | all | 1 | genus 1 curve (11a3) |
| 3.11.186841 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186873 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.186875 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186876 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186878 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186880 | 3 | 11 | 148 | 1 | ✓ | all | 1 | empty |
| 3.11.186882 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186884 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186896 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186898 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186900 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186901 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186909 | 3 | 11 | 148 | 1 | ✓ | all but 2,3 | 1 | rational |
| 3.11.186910 | 3 | 11 | 147 | 1 | ✓ | all but 2 | 1 | point over Q(a)/(a^3 - a^2 + 1) |
| 3.11.186911 | 3 | 11 | 146 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.186912 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.186913 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.186915 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186916 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186917 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186920 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186921 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186922 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186923 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186925 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186926 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186927 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186928 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186932 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.186941 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.186942 | 3 | 11 | 149 | 1 | ✓ | all but 2,3 | 1 | rational |
| 3.11.186943 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186944 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186946 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186947 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.186948 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |