Uniform eventown problems

Let n ≥ k ≥ l ≥ 2 be integers, and let F be a family of k-element subsets of an n-element set. Suppose that l divides the size of the intersection of any two (not necessarily distinct) members in F. We prove that the size of F is at most (⌊n/l⌋ k/l ) provided n is sufficiently large for fixed k and l.

• Type: Journal
• Year: 2016
• Where: EJC
• Authors: Peter Frankl, Norihide Tokushige
• Keywords: EJC 2016, Information Technology