Polynomial Extension of the Stronger Central Sets Theorem

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 ex...

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Bibliographic Details
Published inThe Electronic journal of combinatorics Vol. 30; no. 4
Main Authors Goswami, Sayan, Lorenzo Luperi Baglini, Patra, Sourav Kanti
Format Journal Article
LanguageEnglish
Published 01.12.2023
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Summary: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.
ISSN:1077-8926
1077-8926
DOI:10.37236/11556