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

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.

Final version, which appears in PUMP Journal of Undergraduate Research. (Note: There was a small typo in the published version of Section 7, Numerical Example #1 which has been corrected in this version