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

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

5 Scopus citations

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.

Funding

Partially supported by Israel Science Foundation grant 402/13, United States-Israel Binational Science Foundation grant 2014290, and the Alon Fellowship.

Funders	Funder number
National Science Foundation	DMS-1300120, DMS-1501962, DMS-1201337
United States-Israel Binational Science Foundation	2014290
Israel Science Foundation	1168/15, 402/13

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 - Kahn, Jeff

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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ER -

Chvátal's conjecture and correlation inequalities

Abstract

Bibliographical note

Funding

Keywords

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