Monochromatic sums and quotients in $\mathbb N$

Mauro Di Nasso; Lorenzo Luperi Baglini; Rosario Mennuni; Mariaclara Ragosta; Alessandro Vegnuti

Monochromatic sums and quotients in $\mathbb N$

Logic 2026-04-27 v3 Combinatorics Number Theory

Authors: Mauro Di Nasso , Lorenzo Luperi Baglini , Rosario Mennuni , Mariaclara Ragosta , Alessandro Vegnuti

Abstract

We prove partition regularity of the configuration $x,y,x+y,y/x$ in a strong infinitary form that extends Hindman's Theorem. We study the related issue of partition regularity of configurations involving products of a degree one polynomial in $x$ with one in $y$ , reducing the general problem to a handful of special cases.

Keywords

ramsey theory and colorings partition theory partition congruences

Cite

@article{arxiv.2603.03115,
  title  = {Monochromatic sums and quotients in $\mathbb N$},
  author = {Mauro Di Nasso and Lorenzo Luperi Baglini and Rosario Mennuni and Mariaclara Ragosta and Alessandro Vegnuti},
  journal= {arXiv preprint arXiv:2603.03115},
  year   = {2026}
}

Comments

Added Remark 4.8

Monochromatic sums and quotients in $\mathbb N$

Abstract

Keywords

Cite

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