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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 20,251–20,300
| label ▼ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 4.9.169963 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169962 | 4 | 9 | 107 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169961 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | rational over Q(a)/(a^2 - a + 1) |
| 4.9.169960 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169959 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169958 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.169957 | 4 | 9 | 104 | 1 | ✓ | ∅ | -1 | empty |
| 4.9.169956 | 4 | 9 | 105 | 1 | ✓ | all | 1 | point over Q(a)/(a^2 - a - 1) |
| 4.9.169955 | 4 | 9 | 105 | 1 | ✓ | all | 2 | empty |
| 4.9.169954 | 4 | 9 | 105 | 1 | ✓ | all | 4 | point over Q(a)/(a^2 - a - 1) |
| 4.9.169953 | 4 | 9 | 106 | 1 | ✓ | all | 4 | rational |
| 4.9.169952 | 4 | 9 | 105 | 1 | ✓ | ∅ | -1 | point over Q(a)/(a^2 - a - 1) |
| 4.9.169951 | 4 | 9 | 106 | 1 | ✓ | all | 3 | rational |
| 4.9.169950 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | empty |
| 4.9.169949 | 4 | 9 | 106 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169948 | 4 | 9 | 107 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169947 | 4 | 9 | 105 | 1 | ✓ | all | 1 | point over Q(a)/(a^2 - a + 1) |
| 4.9.169946 | 4 | 9 | 106 | 1 | ✓ | all | 3 | rational |
| 4.9.169945 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169944 | 4 | 9 | 106 | 1 | ✓ | all | 3 | rational |
| 4.9.169943 | 4 | 9 | 107 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169942 | 4 | 9 | 106 | 1 | ✓ | all | 4 | rational |
| 4.9.169941 | 4 | 9 | 106 | 1 | ✓ | all | 3 | rational |
| 4.9.169940 | 4 | 9 | 107 | 1 | ✓ | all but 2 | 2 | rational |
| 4.9.169939 | 4 | 9 | 106 | 1 | ✓ | all | 1 | rational |
| 4.9.169938 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169937 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169936 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169935 | 4 | 9 | 108 | 1 | ✓ | all | 4 | rational |
| 4.9.169934 | 4 | 9 | 105 | 1 | ✓ | all | 3 | point over Q(a)/(a^2 - a - 1) |
| 4.9.169933 | 4 | 9 | 106 | 1 | ✓ | all | 3 | rational over Q(a)/(a^2 - a - 1) |
| 4.9.169932 | 4 | 9 | 106 | 1 | ✓ | all | 4 | rational |
| 4.9.169931 | 4 | 9 | 106 | 1 | ✓ | all | 4 | rational |
| 4.9.169930 | 4 | 9 | 106 | 1 | ✓ | all | 3 | rational |
| 4.9.169929 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |
| 4.9.169928 | 4 | 9 | 106 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169927 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169926 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.169925 | 4 | 9 | 106 | 1 | ✓ | all | 4 | rational |
| 4.9.169924 | 4 | 9 | 107 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.169923 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169922 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169921 | 4 | 9 | 108 | 1 | ✓ | all but 2 | 2 | rational |
| 4.9.169920 | 4 | 9 | 106 | 1 | ✓ | all | 1 | rational |
| 4.9.169919 | 4 | 9 | 107 | 1 | ✓ | all | 3 | rational |
| 4.9.169918 | 4 | 9 | 107 | 1 | ✓ | all | 5 | rational |
| 4.9.169917 | 4 | 9 | 107 | 1 | ✓ | all | 4 | rational |
| 4.9.169916 | 4 | 9 | 107 | 1 | ✓ | all | 5 | rational |
| 4.9.169915 | 4 | 9 | 108 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.169914 | 4 | 9 | 107 | 1 | ✓ | all | 1 | rational |