A Class of Binomial Permutation Polynomials

TL;DR

This paper introduces a new criterion for identifying permutation binomials, leading to the discovery of numerous classes of such polynomials with Niho exponents, expanding the understanding of permutation polynomials.

Contribution

A novel criterion for binomial permutation polynomials is proposed, enabling the construction of many new classes with Niho exponents.

Findings

Many classes of binomial permutation polynomials are obtained.

Several monomial complete permutation polynomials are identified.

The exponents involved are of Niho type.

Abstract

In this note, a criterion for a class of binomials to be permutation polynomials is proposed. As a consequence, many classes of binomial permutation polynomials and monomial complete permutation polynomials are obtained. The exponents in these monomials are of Niho type.