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On Cancellative Set Families

A family of subsets of an n-set is 2-cancellative if, for every four-tuple {A, B, C, D} of its members, A∪ B∪C=A∪ B∪ D implies C = D. This generalizes the concept of cancellative set families, defined by the property that A∪B ≠A ∪ C for A, B, C all different. The asymptotics of the maximum size of cancellative families of subsets of an n-set is known (Tolhuizen [7]). We provide a new upper bound on the size of 2-cancellative families, improving the previous bound of 20.458n to 20.42n.