A new construction for cancellative families of sets

Abstract

Following [2], we say a family, H, of subsets of a n-element set is cancellative if A ∪ B = A ∪ C implies B = C when A, B, C ∈ H. We show how to construct cancellative families of sets with c2.54797n elements. This improves the previous best bound c2.52832n and falsifies conjectures of Erdös and Katona [3] and Bollobas [1].