A new criterion for permutation polynomials
type: Item
instance of: scholarly article
title: A new criterion for permutation polynomials
zbMATH Open document ID: 0817.11055
author: Gerhard Turnwald
published in: Finite Fields and their Applications
publication date: 1995-02-09T00:00:00Z
review text: The author presents the relationships among: (1) the number of distinct values \(v\) of a polynomial \(f(x)\) of degree \(n\) over a finite field of \(q\) elements, (2) the degree \(u\) of the first non-vanishing elementary symmetric function of the values of \(f(x)\), and (3) the degree \(w\) of the first non-vanishing power sum of the values of \(f(x)\). The author provides an easy proof of the theorem of D. Wan: If \(v>q- (q- 1)/n\), then \(v=q\), i.e. \(f(x)\) is a permutation polynomial if \(v>q- (q- 1)/n\). The author also provides many other characterizations of permutation polynomials, as well as various examples and counterexamples.
Mathematics Subject Classification ID: 11T06
zbMATH DE Number: 720503
zbMATH Keywords: finite field
zbMATH Keywords: permutation polynomial
reviewed by: Richard A. Mollin
MaRDI profile type: Publication
full work available at URL: ffta.1995.1005
OpenAlex ID: W2003850720
DOI: 10.1006/FFTA.1995.1005
description: scientific article; zbMATH DE number 720503