Low-degree permutation rational functions over finite fields
Zhiguo Ding, Michael E. Zieve · Acta Arithmetica · 2022
We determine all degree-$4$ rational functions $f(X)\in \mathbb {F}_q(X)$ which permute $\mathbb {P}^1(\mathbb {F}_q)$, and answer two questions of Ferraguti and Micheli about the number of such functions and the number of equivalence classes of such func