Label

The short label of a matroid, of the form {rank}.{n}.{seq}, e.g. 3.7.13. Here rank is the rank, n is the ground set size, and seq is the 0-based position of the record when all matroids of that rank and size are sorted by id.

Ids sort with * before 0, so seq 0 is always the uniform matroid $U_{r,n}$, whose revlex encoding is all *. The id is the canonical identifier and determines the matroid on its own.