Potentially eventually exponentially positive sign patterns

Abstract

We introduce the study of potentially eventually exponentially positive (PEEP) sign patterns and establish several results using the connections between these sign patterns and the potentially eventually positive (PEP) sign patterns. It is shown that the problem of characterizing PEEP sign patterns is not equivalent to that of characterizing PEP sign patterns. A characterization of all $2\times 2$ and $3\times 3$ PEEP sign patterns is given.