On the exponent set of nonnegative primitive tensors

TL;DR

This paper characterizes the conditions under which nonnegative tensors are primitive and determines their exponent set, revealing it as a specific integer range for tensors with certain order and dimension.

Contribution

It provides a necessary and sufficient condition for nonnegative tensors to be primitive and explicitly describes their exponent set.

Findings

Exponent set of nonnegative primitive tensors is {1, 2, er (n-1)^2+1} for tensors with order m(a0a0a0a0n) and dimension n.

Established a precise characterization of when a nonnegative tensor is primitive.

Determined the exact range of exponents for primitive tensors of given order and dimension.

Abstract

In this paper, we present a necessary and sufficient condition for a nonnegative tensor to be a primitive one, show that the exponent set of nonnegative primitive tensors with order $m(\ge n)$ and dimension $n$ is $\{k| 1\le k\le (n-1)^2+1\}. $