Chvátal's conjecture and correlation inequalities

Abstract Chvatal's conjecture in extremal combinatorics asserts that for any decreasing family F of subsets of a finite set S , there is a largest intersecting subfamily of F consisting of all members of F that include a particular x ∈ S . In this paper we reformulate the conjecture in terms of influences of variables on Boolean functions and correlation inequalities, and study special cases and variants using tools from discrete Fourier analysis.