Chvatal's conjecture and correlation inequalities

Ehud Friedgut; Jeff Kahn; Gil Kalai; Nathan Keller

doi:10.1016/j.jcta.2017.11.015

Chvatal's conjecture and correlation inequalities

Ehud Friedgut, Jeff Kahn, Gil Kalai, Nathan Keller

Weizmann Institute of Science, Bar-Ilan University, The Hebrew University of Jerusalem

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

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 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.

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

Keywords

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

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1016/j.jcta.2017.11.015

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title = "Chvatal'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 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.",

keywords = "Chv{\'a}tal's conjecture, Correlation inequalities, Discrete Fourier analysis, Extremal combinatorics, Influences",

author = "Ehud Friedgut and Jeff Kahn and Gil Kalai and Nathan Keller",

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year = "2018",

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doi = "10.1016/j.jcta.2017.11.015",

language = "الإنجليزيّة",

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T1 - Chvatal's conjecture and correlation inequalities

AU - Friedgut, Ehud

AU - Kahn, Jeff

AU - Kalai, Gil

AU - Keller, Nathan

PY - 2018/5

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N2 - 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.

AB - 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.

KW - Chvátal's conjecture

KW - Correlation inequalities

KW - Discrete Fourier analysis

KW - Extremal combinatorics

KW - Influences

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U2 - 10.1016/j.jcta.2017.11.015

DO - 10.1016/j.jcta.2017.11.015

M3 - مقالة

SN - 0097-3165

VL - 156

SP - 22

EP - 43

JO - Journal Of Combinatorial Theory Series A

JF - Journal Of Combinatorial Theory Series A

ER -

Chvatal's conjecture and correlation inequalities

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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