Vol. 4, No. 4, 2011

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ISSN: 1944-4184 (e-only)
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Constructions of potentially eventually positive sign patterns with reducible positive part

Marie Archer, Minerva Catral, Craig Erickson, Rana Haber, Leslie Hogben, Xavier Martinez-Rivera and Antonio Ochoa

Vol. 4 (2011), No. 4, 405–410
Abstract

Potentially eventually positive (PEP) sign patterns were introduced by Berman et al. (Electron. J. Linear Algebra 19 (2010), 108–120), where it was noted that a matrix is PEP if its positive part is primitive, and an example was given of a 3 × 3 PEP sign pattern with reducible positive part. We extend these results by constructing n × n PEP sign patterns with reducible positive part, for every n 3.

Keywords
potentially eventually positive, PEP, sign pattern, matrix, digraph
Mathematical Subject Classification 2010
Primary: 15B35, 15B48, 05C50, 15A18
Milestones
Received: 3 March 2011
Accepted: 10 June 2011
Published: 21 March 2012

Communicated by Chi-Kwong Li
Authors
Marie Archer
Department of Mathematics
Iowa State University of Science and Technology
396 Carver Hall
Ames, IA 50011-2064
United States
Department of Mathematics
Columbia College
Columbia, SC 29203
United States
Minerva Catral
Department of Mathematics and Computer Science
Xavier University
Cincinnati, OH 45207
United States
Craig Erickson
Department of Mathematics
Iowa State University of Science and Technology
396 Carver Hall
Ames, IA 50011-2064
United States
Rana Haber
Mathematics Department
Florida Institute of Technology
Melbourne, FL 32901
United States
Leslie Hogben
Department of Mathematics
Iowa State University of Science and Technology
396 Carver Hall
Ames, IA 50011-2064
United States
American Institute of Mathematics
360 Portage Avenue
Palo Alto, CA 94306
United States
Xavier Martinez-Rivera
Department of Mathematical Sciences
University of Puerto Rico
Mayagüez, P.R. 00681
United States
Antonio Ochoa
California State Polytechnic University, Pomona
Pomona, CA 91768
United States