Set-Systems with Restricted Multiple Intersections

We give a generalization for the Deza-Frankl-Singhi Theorem in case of multiple intersections. More exactly, we prove, that if H is a set-system, which satisfies that for some k, the k-wise intersections occupy only residue-classes modulo a p prime, while the sizes of the members of H are not in these residue classes, then the size of H is at most (k - 1) i=0 n i This result considerably strengthens an upper bound of F

• Type: Journal
• Year: 2002
• Where: COMBINATORICS
• Authors: Vince Grolmusz
• Keywords: COMBINATORICS 2002, Deza-Frankl-Singhi Theorem, K-wise Intersections, Multiple Intersections