Rational functions of Degree Four that Permute the Projective Line over a Finite Field

Abstract

Recently, rational functions of degree three that permute the projective line ${\mathbb{P}}^1({\mathbb{F}}_q)$ over a finite field ${\mathbb{F}}_q$ were determined by Ferraguti and Micheli. In the present paper, using a different method, we determine all rational functions of degree four that permute the ${\mathbb{P}}^1({\mathbb{F}}_q)$.

12 pages. Sporadic PRs with small q's are determines. Typos in v1 are corrected

References in corpus (1)

• A power sum formula by Carlitz and its applications to permutation rational functions of finite fields

Cited by in corpus (2)

• Low-degree permutation rational functions over finite fields
• A new family of exceptional rational functions