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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.
8,076,768 matroids, showing 20,601–20,650
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.91832 | 3 | 11 | 151 | 1 | ✓ | all | 2 | rational |
| 3.11.91836 | 3 | 11 | 151 | 1 | ✓ | all | 2 | rational |
| 3.11.91837 | 3 | 11 | 151 | 1 | ✓ | all | 2 | rational |
| 3.11.91838 | 3 | 11 | 151 | 1 | ✓ | all | 2 | rational |
| 3.11.91839 | 3 | 11 | 151 | 1 | ✓ | all | 2 | empty |
| 3.11.91841 | 3 | 11 | 151 | 1 | ✓ | all | 2 | rational |
| 3.11.91845 | 3 | 11 | 150 | 1 | ✓ | all | 2 | rational |
| 3.11.91846 | 3 | 11 | 152 | 1 | ✓ | all | 2 | rational |
| 3.11.91849 | 3 | 11 | 151 | 1 | ✓ | all | 2 | rational |
| 3.11.91850 | 3 | 11 | 151 | 1 | ✓ | all | 2 | rational |
| 3.11.91851 | 3 | 11 | 150 | 1 | ✓ | all | 2 | rational |
| 3.11.91852 | 3 | 11 | 151 | 1 | ✓ | all | 2 | rational |
| 3.11.91853 | 3 | 11 | 150 | 1 | ✓ | all | 2 | genus 1 curve (15a8) |
| 3.11.91857 | 3 | 11 | 149 | 1 | ✓ | all | 2 | rational |
| 3.11.91860 | 3 | 11 | 151 | 1 | ✓ | all | 2 | rational |
| 3.11.91864 | 3 | 11 | 152 | 1 | ✓ | all | 2 | rational |
| 3.11.91869 | 3 | 11 | 151 | 1 | ✓ | all | 2 | rational |
| 3.11.91870 | 3 | 11 | 150 | 1 | ✓ | all | 2 | rational |
| 3.11.91871 | 3 | 11 | 150 | 1 | ✓ | all | 2 | rational |
| 3.11.91872 | 3 | 11 | 152 | 1 | ✓ | all | 2 | rational |
| 3.11.91880 | 3 | 11 | 150 | 1 | ✓ | all | 2 | rational |
| 3.11.91882 | 3 | 11 | 150 | 1 | ✓ | all | 2 | rational |
| 3.11.91883 | 3 | 11 | 151 | 1 | ✓ | all | 2 | rational |
| 3.11.91885 | 3 | 11 | 150 | 1 | ✓ | all | 2 | rational |
| 3.11.91887 | 3 | 11 | 150 | 1 | ✓ | all | 2 | empty |
| 3.11.91889 | 3 | 11 | 150 | 1 | ✓ | all | 2 | rational |
| 3.11.91892 | 3 | 11 | 149 | 1 | ✓ | all | 2 | point over Q(a)/(a^2 - a + 2) |
| 3.11.91894 | 3 | 11 | 149 | 1 | ✓ | all | 2 | empty |
| 3.11.91896 | 3 | 11 | 151 | 1 | ✓ | all | 2 | rational |
| 3.11.91898 | 3 | 11 | 150 | 1 | ✓ | all | 2 | rational |
| 3.11.91900 | 3 | 11 | 149 | 1 | ✓ | all | 2 | empty |
| 3.11.91910 | 3 | 11 | 149 | 1 | ✓ | all | 2 | point over Q(a)/(a^3 - a^2 + 1) |
| 3.11.91920 | 3 | 11 | 150 | 1 | ✓ | all | 2 | rational |
| 3.11.91922 | 3 | 11 | 152 | 2 | ✓ | all | 2 | rational |
| 3.11.91923 | 3 | 11 | 152 | 1 | ✓ | all | 2 | rational |
| 3.11.91925 | 3 | 11 | 151 | 1 | ✓ | all | 2 | rational |
| 3.11.91926 | 3 | 11 | 152 | 1 | ✓ | all | 2 | rational |
| 3.11.91927 | 3 | 11 | 151 | 1 | ✓ | all | 2 | rational |
| 3.11.91929 | 3 | 11 | 152 | 1 | ✓ | all | 2 | rational |
| 3.11.91930 | 3 | 11 | 151 | 1 | ✓ | all | 2 | rational |
| 3.11.91931 | 3 | 11 | 151 | 1 | ✓ | all | 2 | rational |
| 3.11.91932 | 3 | 11 | 151 | 1 | ✓ | all | 2 | rational |
| 3.11.91935 | 3 | 11 | 151 | 2 | ✓ | all | 2 | rational |
| 3.11.91938 | 3 | 11 | 150 | 1 | ✓ | all | 2 | rational |
| 3.11.91939 | 3 | 11 | 150 | 2 | ✓ | all | 2 | empty |
| 3.11.91940 | 3 | 11 | 152 | 1 | ✓ | all | 2 | rational |
| 3.11.91941 | 3 | 11 | 151 | 1 | ✓ | all | 2 | rational |
| 3.11.91946 | 3 | 11 | 150 | 1 | ✓ | all | 2 | rational |
| 3.11.91951 | 3 | 11 | 150 | 2 | ✓ | all | 2 | rational |
| 3.11.91953 | 3 | 11 | 152 | 1 | ✓ | all | 2 | rational |