An Upper Bound on the Sizes of Multiset-Union-Free Families

Abstract

Let F[subscript 1] and F[subscript 2] be two families of subsets of an n-element set. We say that F[subscript 1] and F[subscript 2] are multiset-union-free if for any A, B ∈ F[subscript 1] and C, D ∈ F[subscript 2] the multisets A ⊎ C and B ⊎ D are different, unless both A = B and C = D. We derive a new upper bound on the maximal sizes of multiset-union-free pairs, improving a result of Urbanke and Li.