Monochromatic sums equal to products near zero

Sourav Kanti Patra; Md Moid Shaikh

Monochromatic sums equal to products near zero

Combinatorics 2020-11-17 v1

Authors: Sourav Kanti Patra , Md Moid Shaikh

Abstract

Hindman proved that, whenever the set $\mathbb{N}$ of naturals is finitely colored, there must exist non-constant monochromatic solution of the equation $a+b=cd$ . In this paper we extend this result for dense subsemigroups of $((0, \infty), +)$ to near zero.

Keywords

monochromatic solutions sums equal to products near zero Hindman's theorem Ramsey theory dense subsemigroups finite coloring

Cite

@article{arxiv.1906.04621,
  title  = {Monochromatic sums equal to products near zero},
  author = {Sourav Kanti Patra and Md Moid Shaikh},
  journal= {arXiv preprint arXiv:1906.04621},
  year   = {2020}
}

Comments

9 pages

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