Polynomials in $\mathbb{F}_p[x]$ which commute under composition

Jeffrey Hatley; Mayah Teplitskiy

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arXiv · 2206.05349

Polynomials in $\mathbb{F}_p[x]$ which commute under composition

Jeffrey Hatley·Mayah Teplitskiy

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Abstract

Let $\mathbb{F}$ be a finite field and let $f$ be a linear polynomial in $\mathbb{F}[x]$. We investigate the number of polynomials of degree $d$ which commute with $f$ under composition. In so doing, we rediscover a result of Park, but with a conceptually simpler proof.

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Jeffrey Hatley, Mayah Teplitskiy. 2022-06-10. Polynomials in $\mathbb{F}_p[x]$ which commute under composition. https://arxiv.org/abs/2206.05349

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