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arXiv · 2506.00369

The Interplay between Additive and Multiplicative Central Sets Theorems

Pintu Debnath·Sayan Goswami·Chunlin Liu
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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--\v{C}ech compactification. In this article, we establish a unified version of the Central Sets Theorem that simultaneously captures both additive and multiplicative structures.

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Pintu Debnath, Sayan Goswami, Chunlin Liu. 2025-05-31. The Interplay between Additive and Multiplicative Central Sets Theorems. https://arxiv.org/abs/2506.00369

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