A quasi-stability result for dictatorships in S  n

David Ellis; Yuval Filmus; Ehud Friedgut

doi:10.1007/s00493-014-3027-1

A quasi-stability result for dictatorships in S _n

David Ellis, Yuval Filmus, Ehud Friedgut

Department of Mathematics

Weizmann Institute of Science

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

Abstract

We prove that Boolean functions on S_n whose Fourier transform is highly concentrated on the first two irreducible representations of S_n, are close to being unions of cosets of point-stabilizers. We use this to give a natural proof of a stability result on intersecting families of permutations, originally conjectured by Cameron and Ku [6], and first proved in [10]. We also use it to prove a ‘quasi-stability’ result for an edge-isoperimetric inequality in the transposition graph on S_n, namely that subsets of S_n with small edge-boundary in the transposition graph are close to being unions of cosets of point-stabilizers.

Original language	English
Pages (from-to)	573-618
Number of pages	46
Journal	Combinatorica
Volume	35
Issue number	5
DOIs	https://doi.org/10.1007/s00493-014-3027-1
State	Published - 1 Oct 2015

All Science Journal Classification (ASJC) codes

Computational Mathematics
Discrete Mathematics and Combinatorics

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title = "A quasi-stability result for dictatorships in S n",

abstract = "We prove that Boolean functions on Sn whose Fourier transform is highly concentrated on the first two irreducible representations of Sn, are close to being unions of cosets of point-stabilizers. We use this to give a natural proof of a stability result on intersecting families of permutations, originally conjectured by Cameron and Ku [6], and first proved in [10]. We also use it to prove a {\textquoteleft}quasi-stability{\textquoteright} result for an edge-isoperimetric inequality in the transposition graph on Sn, namely that subsets of Sn with small edge-boundary in the transposition graph are close to being unions of cosets of point-stabilizers.",

author = "David Ellis and Yuval Filmus and Ehud Friedgut",

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AU - Friedgut, Ehud

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N2 - We prove that Boolean functions on Sn whose Fourier transform is highly concentrated on the first two irreducible representations of Sn, are close to being unions of cosets of point-stabilizers. We use this to give a natural proof of a stability result on intersecting families of permutations, originally conjectured by Cameron and Ku [6], and first proved in [10]. We also use it to prove a ‘quasi-stability’ result for an edge-isoperimetric inequality in the transposition graph on Sn, namely that subsets of Sn with small edge-boundary in the transposition graph are close to being unions of cosets of point-stabilizers.

AB - We prove that Boolean functions on Sn whose Fourier transform is highly concentrated on the first two irreducible representations of Sn, are close to being unions of cosets of point-stabilizers. We use this to give a natural proof of a stability result on intersecting families of permutations, originally conjectured by Cameron and Ku [6], and first proved in [10]. We also use it to prove a ‘quasi-stability’ result for an edge-isoperimetric inequality in the transposition graph on Sn, namely that subsets of Sn with small edge-boundary in the transposition graph are close to being unions of cosets of point-stabilizers.

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DO - 10.1007/s00493-014-3027-1

M3 - مقالة

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JO - Combinatorica

JF - Combinatorica

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ER -

A quasi-stability result for dictatorships in S _n

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