A QUASI-STABILITY RESULT FOR DICTATORSHIPS IN Sri DAVID ELLIS, YUVAL FILMUS, EHUD FRIEDGUT

David Ellis, Yuval Filmus, Ehud Friedgut

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)573-618
Number of pages46
JournalCombinatorica
Volume35
Issue number5
DOIs
StatePublished - Oct 2015

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