Sign patterns that require or allow power-positivity

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Minerva Catral
Leslie Hogben
Dale D. Olesky
Pauline van den Driessche


A matrix A is power-positive if some positive integer power of A is entrywise positive. A sign pattern A is shown to require power-positivity if and only if either A or −A is nonnegative and has a primitive digraph, or equivalently, either A or −A requires eventual positivity. A sign pattern A is shown to be potentially power-positive if and only if A or −A is potentially eventually positive.

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