Chvatal's conjecture and correlation inequalities

摘要

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 is an element of 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. (C) 2017 Elsevier Inc. All rights reserved.