Frankl-Füredi Type Inequalities for Polynomial Semi-lattices

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 6= 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| ≤ ∑ki=0 (n−1 i ). 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. §