Matroid id

The canonical identifier r{rank}_n{n}_{revlex}, where {revlex} is polyDB's REVLEX_BASIS_ENCODING of the matroid (see revlex encoding). Among all relabelings of the ground set, the lexicographically minimal encoding (comparing with 0 < *) is chosen, so the id is an isomorphism invariant: two matroids get the same id exactly when they are isomorphic.

The id alone reconstructs the matroid, with no other data needed, and it matches the key used by polyDB. Example: r3_n4_0*** is the rank-3 matroid on 4 elements whose only non-basis is $\{1,2,3\}$.

Full details: schema.md.