PublicationsPapers

Boolean functions on $S_n$ which are nearly linear

Yuval Filmus
Discrete Analysis 2021:25

We show that a function $f\colon S_n \to \{0,1\}$ which is close to degree 1 is close to a union of an almost-disjoint family of cosets. Our characterization is tight: any union of an almost-disjoint family of cosets is close to degree 1. This improves on our earlier work with David Ellis and Ehud Friedgut.

We complement this result, which is about the $L_2$ metric, with similar results in the $L_0$ and $L_\infty$ metrics.

BibTeX

@article{Filmus2021,
  title = {Boolean functions on {$S_n$} which are nearly linear},
  author = {Yuval Filmus},
  journal = {Discrete Analysis},
  year = {2021},
  pages = {25:1--25:27}
}
copy to clipboard