The stability of finite sets in dyadic groups

Abstract

We show that there is an absolute $c>0$ such that any subset of ${\mathbb{F}}_2^{\infty }$ of size $N$ is $O(N^{1-c})$-stable in the sense of Terry and Wolf. By contrast a size $N$ arithmetic progression in the integers is not $N$-stable.

9 pp; corrected some errors and expanded the introduction

References in corpus (3)

• Progression-free sets in Z_4^n are exponentially small
• On cap sets and the group-theoretic approach to matrix multiplication
• On large subsets of $F_q^n$ with no three-term arithmetic progression