Polynomial extension of the Stronger Central Sets Theorem

2022/09/21 by Sayan Goswami, Goswami, Sayan, Lorenzo Luperi Baglini +3
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2209.10253

openalex publication_date 2022/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In [F81] Furstenberg introduced the notion of central set and established his famous Central Sets Theorem. Since then, several improved versions of Furstenberg's result have been found. The strongest generalization has been published by De, Hindman and Strauss in [DHS08], whilst a polynomial extension by Bergelson, Johnson and Moreira appeared in [BJM17]. In this article, we will establish a polynomial extension of the stronger version of the central sets theorem, and we will discuss properties of the families of sets that this result leads to consider

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