Polynomials in Fp[x] Which Commute Under Composition

Keywords: polynomials; finite fields; composition of functions; combinatorics


Let F be a finite field and let f be a linear polynomial in 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.

Author Biographies

Jeffrey Hatley, Union College

Assistant professor of mathematics at Union College

Mayah Teplitskiy, Union College

Undergraduate student

How to Cite
Hatley, J., & Teplitskiy, M. (2023). Polynomials in Fp[x] Which Commute Under Composition. The PUMP Journal of Undergraduate Research, 6, 102-114. Retrieved from https://journals.calstate.edu/pump/article/view/3611