#### Vol. 4, No. 4, 2011

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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 $n\ge 3$.

##### 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