New result and some open problems on the primitive degree of nonnegative tensors

TL;DR

This paper establishes the complete set of possible exponents for nonnegative primitive tensors of order m≥3 and dimension n, and discusses open problems for future research in tensor theory.

Contribution

It determines the exact exponent set for nonnegative primitive tensors and introduces open problems, advancing understanding in tensor primitive degree.

Findings

Exponent set for nonnegative primitive tensors is {1, 2, ..., (n-1)^2+1}

Provides a complete characterization of tensor primitive degrees for specified tensors

Proposes open problems for further exploration in tensor theory

Abstract

In this paper, we show that the exponent set of nonnegative primitive tensors with order m(\geq 3) and dimension n is {1,2,\ldots, (n-1)^2+1}; and propose some open problems for further research.