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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 21,301–21,350
| label ▼ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 4.9.168913 | 4 | 9 | 108 | 1 | ✓ | all | 7 | rational |
| 4.9.168912 | 4 | 9 | 109 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.168911 | 4 | 9 | 108 | 1 | ✓ | all | 6 | rational |
| 4.9.168910 | 4 | 9 | 108 | 1 | ✓ | all but 2 | 3 | rational |
| 4.9.168909 | 4 | 9 | 109 | 1 | ✓ | all | 6 | rational |
| 4.9.168908 | 4 | 9 | 109 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.168907 | 4 | 9 | 109 | 1 | ✓ | all | 4 | rational |
| 4.9.168906 | 4 | 9 | 109 | 1 | ✓ | all | 3 | rational |
| 4.9.168905 | 4 | 9 | 110 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.168904 | 4 | 9 | 108 | 2 | ✓ | all but 2,3,5,7 | 0 | rational |
| 4.9.168903 | 4 | 9 | 108 | 2 | ✓ | all | 0 | rational |
| 4.9.168902 | 4 | 9 | 108 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.168901 | 4 | 9 | 109 | 2 | ✓ | ∅ | -1 | rational |
| 4.9.168900 | 4 | 9 | 107 | 1 | ✓ | all | 2 | rational |
| 4.9.168899 | 4 | 9 | 108 | 2 | ✓ | all but 2 | 1 | rational |
| 4.9.168898 | 4 | 9 | 108 | 2 | ✓ | all | 2 | rational |
| 4.9.168897 | 4 | 9 | 107 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.168896 | 4 | 9 | 108 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.168895 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.168894 | 4 | 9 | 109 | 2 | ✓ | {3} | -1 | rational |
| 4.9.168893 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.168892 | 4 | 9 | 109 | 2 | ✓ | all but 2 | 2 | rational |
| 4.9.168891 | 4 | 9 | 109 | 2 | ✓ | all | 2 | rational |
| 4.9.168890 | 4 | 9 | 108 | 1 | ✓ | all | 1 | rational |
| 4.9.168889 | 4 | 9 | 109 | 2 | ✓ | ∅ | -1 | rational |
| 4.9.168888 | 4 | 9 | 108 | 1 | ✓ | all | 1 | rational |
| 4.9.168887 | 4 | 9 | 109 | 2 | ✓ | all | 3 | rational |
| 4.9.168886 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.168885 | 4 | 9 | 109 | 1 | ✓ | all but 2,3,5 | 0 | rational |
| 4.9.168884 | 4 | 9 | 109 | 1 | ✓ | all | 2 | rational |
| 4.9.168883 | 4 | 9 | 110 | 2 | ✓ | ∅ | -1 | rational |
| 4.9.168882 | 4 | 9 | 108 | 1 | ✓ | ∅ | -1 | rational |
| 4.9.168881 | 4 | 9 | 109 | 2 | ✓ | all but 2,3 | 1 | rational |
| 4.9.168880 | 4 | 9 | 109 | 2 | ✓ | all | 2 | rational |
| 4.9.168879 | 4 | 9 | 108 | 1 | ✓ | all | 3 | rational |
| 4.9.168878 | 4 | 9 | 109 | 1 | ✓ | all but 2 | 2 | rational |
| 4.9.168877 | 4 | 9 | 109 | 1 | ✓ | all | 4 | rational |
| 4.9.168876 | 4 | 9 | 110 | 2 | ✓ | all | 2 | rational |
| 4.9.168875 | 4 | 9 | 108 | 1 | ✓ | all but 2,3,5 | 0 | rational |
| 4.9.168874 | 4 | 9 | 109 | 2 | ✓ | all but 2 | 1 | rational |
| 4.9.168873 | 4 | 9 | 109 | 2 | ✓ | all but 2 | 2 | rational |
| 4.9.168872 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |
| 4.9.168871 | 4 | 9 | 109 | 1 | ✓ | all but 2,3 | 1 | rational |
| 4.9.168870 | 4 | 9 | 109 | 1 | ✓ | all but 2 | 1 | rational |
| 4.9.168869 | 4 | 9 | 110 | 2 | ✓ | all | 5 | rational |
| 4.9.168868 | 4 | 9 | 108 | 1 | ✓ | all | 2 | rational |
| 4.9.168867 | 4 | 9 | 109 | 1 | ✓ | all but 2 | 2 | rational |
| 4.9.168866 | 4 | 9 | 109 | 1 | ✓ | all | 3 | rational |
| 4.9.168865 | 4 | 9 | 110 | 2 | ✓ | ∅ | -1 | rational |
| 4.9.168864 | 4 | 9 | 109 | 1 | ✓ | all | 3 | rational |