Frankl-Füredi type inequalities for polynomial semi-lattices

Abstract

Let X be an n-set and L a set of nonnegative integers. F, a set of subsets of X, is said to be an L-intersection family if and only if for all E ≠ F ∈ F, |E∩F| ∈ L. A special case of a conjecture of Frankl and Füredi [4] states that if L = {1,2,..., k}, k a positive integer, then |F| ≤ ∑i-0k (in-1). Here |F| denotes the number of elements in F. Recently Ramanan proved this conjecture in [6] We extend his method to polynomial semi-lattices and we also study some special L-intersection families on polynomial semi-lattices. Finally we prove two modular versions of Ray-Chaudhuri-Wilson inequality for polynomial semi-lattices.