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arXiv · 2006.01041

A tight structure theorem for sumsets

Andrew Granville·Aled Walker
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Abstract

Let $A = \{0 = a_0 < a_1 < \cdots < a_{\ell + 1} = b\}$ be a finite set of non-negative integers. We prove that the sumset $NA$ has a certain easily-described structure, provided that $N \geqslant b-\ell$, as recently conjectured by Shakan and the first author. We also classify those sets $A$ for which this bound cannot be improved.

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Andrew Granville, Aled Walker. 2020-06-01. A tight structure theorem for sumsets. https://arxiv.org/abs/2006.01041

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