Chv\'{a}tal's Conjecture and Correlation Inequalities

Ehud Friedgut; Jeff Kahn; Gil Kalai; Nathan Keller

Chv\'{a}tal's Conjecture and Correlation Inequalities

Combinatorics 2016-09-01 v1

Authors: Ehud Friedgut , Jeff Kahn , Gil Kalai , Nathan Keller

Abstract

Chv\'{a}tal's conjecture in extremal combinatorics asserts that for any decreasing family $\mathcal{F}$ of subsets of a finite set $S$ , there is a largest intersecting subfamily of $\mathcal{F}$ consisting of all members of $\mathcal{F}$ that include a particular $x \in S$ . 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.

Keywords

intersecting families

Cite

@article{arxiv.1608.08954,
  title  = {Chv\'{a}tal's Conjecture and Correlation Inequalities},
  author = {Ehud Friedgut and Jeff Kahn and Gil Kalai and Nathan Keller},
  journal= {arXiv preprint arXiv:1608.08954},
  year   = {2016}
}

Comments

15 pages

Chv\'{a}tal's Conjecture and Correlation Inequalities

Abstract

Keywords

Cite

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