Ramsey theory for hypergroups

TL;DR

This paper extends Ramsey theory to hypergroups, introducing new concepts like the $eta$-Ramsey hypergroup and exploring polynomial hypergroups, orbit hypergroups, and deformations of semigroups.

Contribution

It introduces the first notions of Ramsey principles for hypergroups, including the $eta$-Ramsey hypergroup, and studies their properties in various hypergroup classes.

Findings

Defined new Ramsey principles for hypergroups.

Analyzed polynomial and orbit hypergroups in this context.

Established foundational results for hypergroup deformations of semigroups.

Abstract

In this paper, Ramsey theory for discrete hypergroups is introduced with emphasis on polynomial hypergroups, discrete orbit hypergroups and hypergroup deformations of semigroups. In this context, new notions of Ramsey principle for hypergroups and $\alpha$-Ramsey hypergroup, $0 \leq \alpha<1,$ are defined and studied.