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arXiv · 2404.01605

Division properties of commuting polynomials

Kimiko Hasegawa·Rin Sugiyama
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Abstract

Polynomials commute under composition are referred to as commuting polynomials. In this paper, we study division properties for commuting polynomials with rational (and integer) coefficients. As a consequence, we show an algebraic particularity of the commuting polynomials coming from weighted sums for cycle graphs with pendant edges (arXiv:2402.07209v1.). We also discuss a set of commuting polynomials over a field of positive characteristic.

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Kimiko Hasegawa, Rin Sugiyama. 2024-04-02. Division properties of commuting polynomials. https://arxiv.org/abs/2404.01605

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