Chvátal's conjecture and correlation inequalities

Ehud Friedgut; Jeff Kahn; Gil Kalai; Nathan Keller

doi:10.1016/j.jcta.2017.11.015

Chvátal's conjecture and correlation inequalities

Ehud Friedgut, Jeff Kahn, Gil Kalai, Nathan Keller

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

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Abstract

Chvátal'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.

Original language	English
Pages (from-to)	22-43
Number of pages	22
Journal	Journal of Combinatorial Theory. Series A
Volume	156
DOIs	https://doi.org/10.1016/j.jcta.2017.11.015
State	Published - May 2018

Bibliographical note

Publisher Copyright:
© 2017 Elsevier Inc.

Keywords

Chvátal's conjecture
Correlation inequalities
Discrete Fourier analysis
Extremal combinatorics
Influences

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10.1016/j.jcta.2017.11.015

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abstract = "Chv{\'a}tal'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.",

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AU - Kalai, Gil

AU - Keller, Nathan

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KW - Chvátal's conjecture

KW - Correlation inequalities

KW - Discrete Fourier analysis

KW - Extremal combinatorics

KW - Influences

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JF - Journal of Combinatorial Theory. Series A

ER -

Chvátal's conjecture and correlation inequalities

Abstract

Bibliographical note

Keywords

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