On set systems without weak 3-Δ-subsystems Original Research Article

A collection of sets is called a weak Δ-system if sizes of all pairwise intersections of these sets coincide. We prove a new upper bound on the function fw(n), the maximal size of a collection of n-element sets no three of which form a weak Δ-system. Namely, we prove that, for every δ > 0. fw(n) = 0(n!12 + b).