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

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Let F₁ and F₂ be two families of subsets of an n-element set. We say that F₁ and F₂ are multiset-union-free if for any A,B∈ F₁ and C,D∈ F₂ 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.