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

Jeffrey Hatley; Mayah Teplitskiy

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

Number Theory 2023-06-16 v3

Authors: Jeffrey Hatley , Mayah Teplitskiy

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.

Keywords

polynomials over finite fields polynomial theory polynomial roots

Cite

@article{arxiv.2206.05349,
  title  = {Polynomials in $\mathbb{F}_p[x]$ which commute under composition},
  author = {Jeffrey Hatley and Mayah Teplitskiy},
  journal= {arXiv preprint arXiv:2206.05349},
  year   = {2023}
}

Comments

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

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

Abstract

Keywords

Cite

Comments

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