Infinite linear patterns in sets of positive density

2025/05/21 by Felipe Hernández, Hernández, Felipe · 1 citation
Mathematics · #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2505.15458

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 Szemerédi's theorem on arithmetic progressions and the recent density finite sums theorem of Kra, Moreira, Richter, and Robertson.

Cited by

• On density analogs of Hindman's finite sums theorem

Related

• Problems on infinite sumset configurations in the integers and beyond
• Abundant configurations in sumsets with one dense summand
• The Density Finite Sums Theorem
• Asymmetric infinite sumsets in large sets of integers
• Finding linear patterns of complexity one