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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.06090 |
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| _version_ | 1866918165306408960 |
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| author | Jafari, Javad Tootkaboni, Mohammad Akbari |
| author_facet | Jafari, Javad Tootkaboni, Mohammad Akbari |
| contents | The polynomial version of van der Waerden's theorem, proved using dynamical systems by V. Bergelson and A. Leibman in 1996, \cite{Bergelson1996}, significantly highlighted the role of dynamical systems in addressing problems related to monochromatic configurations within algebraic structures. In this paper, by introducing symbolic polynomials, we aim to provide an alternative proof of the polynomial version of van der Waerden's theorem relying solely on Stone-Čech compactification of an infinite discrete semigroup. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_06090 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Algebraic Proof of the Polynomial Version of van der Waerden's Theorem Jafari, Javad Tootkaboni, Mohammad Akbari Combinatorics 11B83, 05A17, 54D80, 22A15 The polynomial version of van der Waerden's theorem, proved using dynamical systems by V. Bergelson and A. Leibman in 1996, \cite{Bergelson1996}, significantly highlighted the role of dynamical systems in addressing problems related to monochromatic configurations within algebraic structures. In this paper, by introducing symbolic polynomials, we aim to provide an alternative proof of the polynomial version of van der Waerden's theorem relying solely on Stone-Čech compactification of an infinite discrete semigroup. |
| title | An Algebraic Proof of the Polynomial Version of van der Waerden's Theorem |
| topic | Combinatorics 11B83, 05A17, 54D80, 22A15 |
| url | https://arxiv.org/abs/2508.06090 |