The Interplay between Additive and Multiplicative Central Sets Theorems
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913868746326016 |
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| author | Debnath, Pintu Goswami, Sayan Liu, Chunlin |
| author_facet | Debnath, Pintu Goswami, Sayan Liu, Chunlin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_00369 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Interplay between Additive and Multiplicative Central Sets Theorems Debnath, Pintu Goswami, Sayan Liu, Chunlin Combinatorics 05D10, 22A15, 54D35 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. |
| title | The Interplay between Additive and Multiplicative Central Sets Theorems |
| topic | Combinatorics 05D10, 22A15, 54D35 |
| url | https://arxiv.org/abs/2506.00369 |