Rédei permutations with the same cycle structure

Juliane Capaverde, Ariane M. Masuda, Virgínia M. Rodrigues

Let ${\mathbb{F}}_q$ be the finite field of order $q$, and ${\mathbb{P}}^1({\mathbb{F}}_q)={\mathbb{F}}_q\cup \{\infty \}$. Write $(x+\sqrt{y}{)}^m$ as $N(x,y)+D(x,y)\sqrt{y}$. For $m\in\mathb…