# On inverses of some permutation polynomials over finite fields of characteristic three

## TL;DR

This paper derives explicit inverse formulas for certain permutation polynomials over finite fields of characteristic three using combinatorial and interpolation techniques.

## Contribution

It provides explicit inverse expressions for a class of reversed Dickson and generalized cyclotomic permutation polynomials over characteristic three fields.

## Key findings

- Explicit inverse formulas for specific permutation polynomials
- Application of piecewise, Lagrange interpolation, and Lucas' theorem methods
- Enhanced understanding of permutation polynomial inverses in characteristic three

## Abstract

By using the piecewise method, Lagrange interpolation formula and Lucas' theorem, we determine explicit expressions of the inverses of a class of reversed Dickson permutation polynomials and some classes of generalized cyclotomic mapping permutation polynomials over finite fields of characteristic three.