The stability of finite sets in dyadic groups
Volume 192 / 2020
Acta Arithmetica 192 (2020), 155-164
MSC: Primary 11B30.
DOI: 10.4064/aa181101-11-6
Published online: 18 October 2019
Abstract
We show that there is an absolute $c \gt 0$ 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 $\mathbb Z $ is not $N$-stable.
