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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 22,001–22,050
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.11.183860 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.183862 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.183863 | 3 | 11 | 151 | 1 | ✓ | all | 1 | rational |
| 3.11.183870 | 3 | 11 | 149 | 1 | ✓ | all but 2,3 | 1 | rational |
| 3.11.183871 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.183872 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.183874 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183875 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.183877 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183878 | 3 | 11 | 150 | 1 | ✓ | all but 2,3 | 1 | rational |
| 3.11.183879 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183881 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183882 | 3 | 11 | 151 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.183888 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.183889 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183890 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183893 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.183895 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183896 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.183899 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183900 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.183901 | 3 | 11 | 149 | 1 | ✓ | all but 3 | 1 | rational |
| 3.11.183902 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.183905 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183913 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.183915 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.183918 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183920 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183924 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183925 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.183927 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183929 | 3 | 11 | 148 | 1 | ✓ | all | 1 | rational |
| 3.11.183934 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.183935 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.183939 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.183940 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.183943 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183944 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.183945 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183947 | 3 | 11 | 149 | 1 | ✓ | all but 3 | 1 | rational |
| 3.11.183949 | 3 | 11 | 150 | 1 | ✓ | all | 1 | rational |
| 3.11.183950 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183951 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183953 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183960 | 3 | 11 | 148 | 2 | ✓ | all | 1 | rational |
| 3.11.183961 | 3 | 11 | 151 | 1 | ✓ | all | 1 | rational |
| 3.11.183964 | 3 | 11 | 150 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.183966 | 3 | 11 | 149 | 1 | ✓ | all | 1 | rational |
| 3.11.183969 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |
| 3.11.183971 | 3 | 11 | 149 | 1 | ✓ | all but 2 | 1 | rational |