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Problems on infinite sumset configurations in the integers and beyond

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arxiv 2311.06197 v2 pith:7C2PZZ65 submitted 2023-11-10 math.CO math.NT

Bryna Kra , Joel Moreira , Florian K. Richter , Donald Robertson This is my paper · ORCID
classification math.COmath.NT
keywords infiniteconfigurationsdensityeveryfoundnaturalnumberspositive
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In contrast to finite arithmetic configurations, relatively little is known about which infinite patterns can be found in every set of natural numbers with positive density. Building on recent advances showing infinite sumsets can be found, we explore numerous open problems and obstructions to finding other infinite configurations in every set of natural numbers with positive density.

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  1. Homogeneous Patterns in Ramsey Theory

    math.CO 2025-01 conditional novelty 6.0 of 10

    The paper establishes new partition regularity results for nonlinear equations, including m-degree homogeneous equations with prescribed degree of regularity.

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