Permutation Polynomials and their Compositional Inverses

TL;DR

This paper explores the structure of permutation polynomials over finite fields, proving all are AGW-PPs, extending previous results, and introducing a new method for finding their compositional inverses.

Contribution

It establishes that all permutation polynomials are AGW-PPs, extends existing results to more polynomials, and proposes a novel approach for computing their inverses.

Findings

All permutation polynomials are AGW-PPs.

Extended results to other permutation polynomials.

Developed a new method for finding compositional inverses.

Abstract

In this paper, we prove that every PP is an AGW-PP. We also extend the result of Wan and Lidl to other permutation polynomials over finite fields and determine their group structure. Moreover, we provide a new general method to find the compositional inverses of all PPs, some new PPs and their compositional inverses are given.