Union-free hypergraphs and probability theory
This paper contains new lower and upper bounds on the number of subsets of an n element set one can have so that the union of no two equals that of two others. A new lower bound is obtained when no two unions of any kind are the same; and a new upper bound when no set has the same union with two others. Related problems when the sets have size restrictions are reviewed and some new results obtained. The lower bounds are obtained by probabilistic reasoning, while one upper bound uses an entropy argument and the other follows by an induction.
scientific article; zbMATH DE number 3869378