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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 19,801–19,850
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.7857 | 3 | 11 | 153 | 1 | ✓ | all | 2 | rational |
| 3.11.7858 | 3 | 11 | 159 | 16 | ✓ | all | 8 | rational |
| 3.11.7859 | 3 | 11 | 158 | 4 | ✓ | all | 7 | rational |
| 3.11.7860 | 3 | 11 | 158 | 4 | ✓ | all | 7 | rational |
| 3.11.7861 | 3 | 11 | 158 | 16 | ✓ | all | 7 | rational |
| 3.11.7862 | 3 | 11 | 158 | 4 | ✓ | all | 7 | rational |
| 3.11.7863 | 3 | 11 | 157 | 2 | ✓ | all | 6 | rational |
| 3.11.7864 | 3 | 11 | 157 | 1 | ✓ | all | 6 | rational |
| 3.11.7865 | 3 | 11 | 157 | 4 | ✓ | all | 6 | rational |
| 3.11.7866 | 3 | 11 | 157 | 8 | ✓ | all | 6 | rational |
| 3.11.7867 | 3 | 11 | 156 | 2 | ✓ | all | 5 | rational |
| 3.11.7868 | 3 | 11 | 156 | 8 | ✓ | all | 5 | rational |
| 3.11.7869 | 3 | 11 | 157 | 8 | ✓ | all | 6 | rational |
| 3.11.7870 | 3 | 11 | 156 | 2 | ✓ | all | 5 | rational |
| 3.11.7871 | 3 | 11 | 156 | 8 | ✓ | all | 5 | rational |
| 3.11.7872 | 3 | 11 | 158 | 2 | ✓ | all | 7 | rational |
| 3.11.7873 | 3 | 11 | 157 | 1 | ✓ | all | 6 | rational |
| 3.11.7874 | 3 | 11 | 157 | 2 | ✓ | all | 6 | rational |
| 3.11.7875 | 3 | 11 | 157 | 2 | ✓ | all | 6 | rational |
| 3.11.7876 | 3 | 11 | 157 | 1 | ✓ | all | 6 | rational |
| 3.11.7877 | 3 | 11 | 157 | 2 | ✓ | all | 6 | rational |
| 3.11.7878 | 3 | 11 | 157 | 4 | ✓ | all | 6 | rational |
| 3.11.7879 | 3 | 11 | 156 | 2 | ✓ | all | 5 | rational |
| 3.11.7880 | 3 | 11 | 156 | 2 | ✓ | all | 5 | rational |
| 3.11.7881 | 3 | 11 | 156 | 4 | ✓ | all | 5 | rational |
| 3.11.7882 | 3 | 11 | 157 | 1 | ✓ | all | 6 | rational |
| 3.11.7883 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7884 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7885 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7886 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7887 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7888 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7889 | 3 | 11 | 156 | 2 | ✓ | all | 5 | rational |
| 3.11.7890 | 3 | 11 | 155 | 2 | ✓ | all | 4 | rational |
| 3.11.7891 | 3 | 11 | 155 | 4 | ✓ | all | 4 | rational |
| 3.11.7892 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7893 | 3 | 11 | 155 | 2 | ✓ | all | 4 | rational |
| 3.11.7894 | 3 | 11 | 157 | 2 | ✓ | all | 6 | rational |
| 3.11.7895 | 3 | 11 | 156 | 2 | ✓ | all | 5 | rational |
| 3.11.7896 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7897 | 3 | 11 | 156 | 1 | ✓ | all | 5 | rational |
| 3.11.7898 | 3 | 11 | 156 | 2 | ✓ | all | 5 | rational |
| 3.11.7899 | 3 | 11 | 157 | 4 | ✓ | all | 6 | rational |
| 3.11.7900 | 3 | 11 | 156 | 2 | ✓ | all | 5 | rational |
| 3.11.7901 | 3 | 11 | 156 | 2 | ✓ | all | 5 | rational |
| 3.11.7902 | 3 | 11 | 156 | 4 | ✓ | all | 5 | rational |
| 3.11.7903 | 3 | 11 | 156 | 2 | ✓ | all | 5 | rational |
| 3.11.7904 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7905 | 3 | 11 | 155 | 1 | ✓ | all | 4 | rational |
| 3.11.7906 | 3 | 11 | 155 | 2 | ✓ | all | 4 | rational |