Reversed Dickson polynomials of the (k+1)-th kind over finite fields

TL;DR

This paper studies the permutation properties of reversed Dickson polynomials of the (k+1)-th kind over finite fields, providing a unified framework that generalizes previous results in the area.

Contribution

It introduces a generalized analysis of reversed Dickson polynomials, unifying and extending existing findings on their permutation behavior over finite fields.

Findings

Characterization of permutation behavior of $D_{n,k}(1,x)$

Unified framework for various reversed Dickson polynomials

Generalization of previous results on polynomial permutations

Abstract

We discuss the properties and the permutation behaviour of the reversed Dickson polynomials of the $(k+1)$-th kind $D_{n,k}(1,x)$ over finite fields. The results in this paper unify and generalize several recently discovered results on reversed Dickson polynomials over finite fields.