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