Permutation polynomials with exponents in an arithmetic progression

On the irreducibility of certain polynomials with coefficients as products of terms in an arithmetic progression

We prove the irreducibility of ceratin polynomials whose coefficients are in arithmetic progression with common difference 2 . We use Sylvester type of results on the greatest prime factor of a product with terms in an arithmetic progression and irreducibility results based on Newton Polygons.

Symbolic Polynomials with Sparse Exponents

Earlier work has presented algorithms to factor and compute GCDs of symbolic Laurent polynomials, that is multivariate polynomials whose exponents are integer-valued polynomials. These earlier algorithms had the problem of high computational complexity in the number of exponent variables and their degree. The present paper solves this problem, presenting a method that preserves the structure of...

The Arithmetic of Borcherds’ Exponents

Permutation Polynomials modulo m

This paper mainly studies problems about so called “permutation polynomials modulo m”, polynomials with integer coefficients that can induce bijections over Zm = {0, · · · , m−1}. The necessary and sufficient conditions of permutation polynomials are given, and the number of all permutation polynomials of given degree and the number induced bijections are estimated. A method is proposed to dete...

On inverse permutation polynomials

We give an explicit formula of the inverse polynomial of a permutation polynomial of the form xrf(xs) over a finite field Fq where s | q − 1. This generalizes results in [6] where s = 1 or f = g q−1 s were considered respectively. We also apply our result to several interesting classes of permutation polynomials.