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arXiv · 1803.00498

A proof of a sumset conjecture of Erdős

Joel Moreira·Florian Karl Richter·Donald Robertson
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Abstract

In this paper we show that every set $A \subset \mathbb{N}$ with positive density contains $B+C$ for some pair $B,C$ of infinite subsets of $\mathbb{N}$, settling a conjecture of Erdős. The proof features two different decompositions of an arbitrary bounded sequence into a structured component and a pseudo-random component. Our methods are quite general, allowing us to prove a version of this conjecture for countable amenable groups.

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Joel Moreira, Florian Karl Richter, Donald Robertson. 2019-06-13. A proof of a sumset conjecture of Erdős. https://doi.org/10.4007/annals.2019.189.2.4

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