Constructions of potentially eventually positive sign patterns with reducible positive part

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 $3\times 3$ PEP sign pattern with reducible positive part. We extend these results by constructing $n\times n$ PEP sign patterns with reducible positive part, for every $n\ge 3$.