Vol. 1, No. 2, 2008

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ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Invariant polynomials and minimal zero sequences

Bryson W. Finklea, Terri Moore, Vadim Ponomarenko and Zachary J. Turner

Vol. 1 (2008), No. 2, 159–165
Abstract

A connection is developed between polynomials invariant under abelian permutation of their variables and minimal zero sequences in a finite abelian group. This connection is exploited to count the number of minimal invariant polynomials for various abelian groups.

Keywords
invariant polynomials, minimal zero sequences, finite abelian group, block monoid, zero-sum
Mathematical Subject Classification 2000
Primary: 13A50, 20K01
Secondary: 20M14
Milestones
Received: 28 October 2007
Accepted: 1 November 2007
Published: 1 July 2008

Communicated by Scott Chapman
Authors
Bryson W. Finklea
Terri Moore
Department of Mathematics
University of Nebraska-Lincoln
203 Avery Hall
Lincoln, NE 68588-0130
United States
Vadim Ponomarenko
Department of Mathematics and Statistics
San Diego State University
San Diego, CA 92182
United States
http://www-rohan.sdsu.edu/~vadim
Zachary J. Turner