A combinatorial approach to the stronger Central Sets Theorem for semigroups

TL;DR

This paper presents a new combinatorial proof of a stronger version of the Central Sets Theorem for semigroups, advancing the understanding of combinatorial properties in algebraic and topological dynamics.

Contribution

It introduces a novel combinatorial approach to prove the stronger Central Sets Theorem, improving upon previous algebraic and topological methods.

Findings

Provides a new combinatorial proof of the stronger Central Sets Theorem

Enhances understanding of combinatorial structures in semigroups

Bridges combinatorial and algebraic approaches in topological dynamics

Abstract

H. Furstenberg introduced the notion of central sets in terms of topological dynamics and established the famous Central Sets Theorem. Later in [A new and stronger Central Sets Theorem, Fund. Math. 199 (2008), 155-175], D. De, N. Hindman, and D. Strauss established a stronger version of the Central Sets Theorem that uses the algebra of the Stone-\v Cech compactification of discrete semigroups. In this article, We will provide a new and combinatorial proof of the stronger Central Sets Theorem.