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The stability of finite sets in dyadic groups

Volume 192 / 2020

Tom Sanders Acta Arithmetica 192 (2020), 155-164 MSC: Primary 11B30. DOI: 10.4064/aa181101-11-6 Published online: 18 October 2019


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.


  • Tom SandersMathematical Institute
    University of Oxford
    Radcliffe Observatory Quarter
    Woodstock Road
    Oxford OX2 6GG, United Kingdom

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