The paper introduces symbolic polynomials to present a new proof of van der Waerden's theorem, implying a fresh perspective on dynamiques.
The polynomial version of van der Waerden's theorem, proved using dynamical systems by V. Bergelson and A. Leibman in 1996, {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.
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Jafari et al. (2025) studied this question.
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