Complete enumeration

A list of every matroid of a given rank on a given number of elements, one per isomorphism class, each written as its revlex basis encoding. Each enumeration is named n{n}r{rank}; for example n13r03 holds the 9,156,392,629 matroids of rank 3 on 13 elements.

These lists run to billions or trillions of matroids, far too many to load into the searchable database with invariants. Instead, each one is split into compressed chunk files that you can download and read with matroid-database-client. A matroid's index is its position in the enumeration, in the order the generator produced it.

We can still show any single matroid from an enumeration: paste its encoding on the enumeration's page, or visit /matroid/{id}, and we compute its combinatorics and (for rank 3) its affine diagram from the id. Such a matroid has no label and no stored invariants.

The enumerations were computed with matroid-generator by Giorgos Mousa.