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arXiv · 2505.11233

A note on iterated sumsets races

Paul Péringuey·Anne de Roton
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Abstract

This short note answers a question raised by Nathanson \cite{Nath25} about "races" between iterated sumsets. We prove that for any integer $n$, there are finite sets of integers $A$ and $B$ with same diameter such that the signs of the elements of the sequence $(|hA|-|hB|)_h$ changes at least $n$ times. Kravitz proved in \cite{Kravitz} a much better result. This brief and modest note may serve as a stepping stone towards his work.

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Paul Péringuey, Anne de Roton. 2025-05-16. A note on iterated sumsets races. https://arxiv.org/abs/2505.11233

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