A 2-Isomorphism Theorem for Hypergraphs

One can associate a polymatroid with a hypergraph that naturally generalises the cycle matroid of a graph. Whitneyʹs 2-isomorphism theorem characterises when two graphs have isomorphic cycle matroids. In this paper Whitneyʹs theorem is generalised to hypergraphs and polymatroids by characterising when two hypergraphs have isomorphic associated polymatroids.