Infinite linear patterns in sets of positive density
Dynamical Systems
2026-03-11 v3 Combinatorics
Number Theory
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.
Cite
@article{arxiv.2505.15458,
title = {Infinite linear patterns in sets of positive density},
author = {Felipe Hernández},
journal= {arXiv preprint arXiv:2505.15458},
year = {2026}
}
Comments
Referee's comments were incorporated