English

Problems on infinite sumset configurations in the integers and beyond

Combinatorics 2025-05-15 v2 Number Theory

Abstract

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.

Keywords

Cite

@article{arxiv.2311.06197,
  title  = {Problems on infinite sumset configurations in the integers and beyond},
  author = {Bryna Kra and Joel Moreira and Florian K. Richter and Donald Robertson},
  journal= {arXiv preprint arXiv:2311.06197},
  year   = {2025}
}

Comments

38 pages, minor revisions following referee's comments

R2 v1 2026-06-28T13:17:32.292Z