We investigate fixed points and cycle types of permutation polynomials and complete permutation polynomials arising from reversed Dickson polynomials of the first kind and second kind over $\mathbb{ F}_p$. We also study the permutation behaviour of reversed Dickson polynomials of the first kind and second kind over $\mathbb{ Z}_m$. Moreover, we prove two special cases of a conjecture on the permutation behaviour of reversed Dickson polynomials over $\mathbb{ F}_p$.
Categories: math.NT math.CO