The Interplay between Additive and Multiplicative Central Sets Theorems

2025/05/31 by Debnath, Pintu, Goswami, Sayan, Liu, Chunlin
#05D10 #22A15 #54D35 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.00369

Abstract

The concept of Central sets, introduced by Furstenberg through the framework of topological dynamics, has played a pivotal role in combinatorial number theory. Furstenberg's Central Sets Theorem highlighted their rich combinatorial structure. Later, De, Hindman, and Strauss strengthen this theorem using the algebraic framework of the Stone--Čech compactification. In this article, we establish a unified version of the Central Sets Theorem that simultaneously captures both additive and multiplicative structures.

Citations

• New polynomial and multidimensional extensions of classical partition results
• A dynamical characterization of C sets

Related

• A dynamical characterization of C sets
• A combinatorial approach to central to theorem
• Polynomial extension of the Stronger Central Sets Theorem
• Central sets and substitutive dynamical systems
• Multidimensional central sets theorem near zero