TY - JOUR
T1 - FKN theorem for the multislice, with applications
AU - Filmus, Yuval
N1 - Publisher Copyright:
© Cambridge University Press 2019.
PY - 2019/1/1
Y1 - 2019/1/1
N2 - The Friedgut-Kalai-Naor (FKN) theorem states that if is a Boolean function on the Boolean cube which is close to degree one, then is close to a dictator, a function depending on a single coordinate. The author has extended the theorem to the slice, the subset of the Boolean cube consisting of all vectors with fixed Hamming weight. We extend the theorem further, to the multislice, a multicoloured version of the slice.As an application, we prove a stability version of the edge-isoperimetric inequality for settings of parameters in which the optimal set is a dictator.
AB - The Friedgut-Kalai-Naor (FKN) theorem states that if is a Boolean function on the Boolean cube which is close to degree one, then is close to a dictator, a function depending on a single coordinate. The author has extended the theorem to the slice, the subset of the Boolean cube consisting of all vectors with fixed Hamming weight. We extend the theorem further, to the multislice, a multicoloured version of the slice.As an application, we prove a stability version of the edge-isoperimetric inequality for settings of parameters in which the optimal set is a dictator.
UR - http://www.scopus.com/inward/record.url?scp=85074127968&partnerID=8YFLogxK
U2 - 10.1017/S0963548319000361
DO - 10.1017/S0963548319000361
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:85074127968
SN - 0963-5483
JO - Combinatorics Probability and Computing
JF - Combinatorics Probability and Computing
ER -