Infinite linear patterns in sets of positive density

Felipe Hernández

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arXiv · 2505.15458

Infinite linear patterns in sets of positive density

Felipe Hernández

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Abstract

In this article we describe all possible infinite linear configurations that can be found in a shift of any set of positive upper Banach density. This simultaneously generalizes Szemer\'edi's theorem on arithmetic progressions and the recent density finite sums theorem of Kra, Moreira, Richter, and Robertson.

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BibTeX RIS

Felipe Hernández. 2025-05-21. Infinite linear patterns in sets of positive density. https://arxiv.org/abs/2505.15458

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