TY - JOUR
T1 - A quasi-stability result for dictatorships in S n
AU - Ellis, David
AU - Filmus, Yuval
AU - Friedgut, Ehud
N1 - Publisher Copyright:
© 2014, János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg.
PY - 2015/10/1
Y1 - 2015/10/1
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.
UR - http://www.scopus.com/inward/record.url?scp=84952309298&partnerID=8YFLogxK
U2 - 10.1007/s00493-014-3027-1
DO - 10.1007/s00493-014-3027-1
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AN - SCOPUS:84952309298
SN - 0209-9683
VL - 35
SP - 573
EP - 618
JO - Combinatorica
JF - Combinatorica
IS - 5
ER -