FKN, first proof, rewritten
Combinatorics
2021-05-10 v1
Abstract
About twenty years ago we wrote a paper, "Boolean Functions whose Fourier Transform is Concentrated on the First Two Levels", \cite{FKN}. In it we offered several proofs of the statement that Boolean functions , whose Fourier coefficients are concentrated on the lowest two levels are close to a constant function or to a function of the form or . Returning to the paper lately, we noticed that the presentation of the first proof is rather cumbersome, and includes several typos. In this note we rewrite that proof, as a service to the public.
Keywords
Cite
@article{arxiv.2105.03246,
title = {FKN, first proof, rewritten},
author = {Ehud Friedgut and GIl Kalai and Assaf Naor},
journal= {arXiv preprint arXiv:2105.03246},
year = {2021}
}