Matroid database
A prototype browser for a collection of 32,400,859 matroids of rank 2, 3 and 4
on up to 11 elements, with their invariants, characteristic sets and
realization spaces. Each matroid has a label
rank.n.seq and a canonical id.
Beyond these, complete enumerations of 3.2 trillion more matroids are available for download. They are far too many to search, but any of them can be viewed by its id.
Browse by rank and size
| rank \ n | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2 | 1 | 3 | 7 | 13 | 23 | 37 | 58 | |||||
| 3 | 1 | 4 | 13 | 38 | 108 | 325 | 1,275 | 10,037 | 298,491 | 31,899,134 | 9,156,392,629* | |
| 4 | 1 | 5 | 23 | 108 | 940 | 190,214 | 4,886,380,924* | |||||
| 5 | 3,222,227,959,444* | |||||||||||
| 6 | 4,886,380,924* |
* Complete enumeration: listed and downloadable, but not in the searchable database.