A bound on the exponent of primitivity in terms of diameter
type: Item
instance of: scholarly article
title: A bound on the exponent of primitivity in terms of diameter
zbMATH Open document ID: 0860.15024
DOI: 10.1016/0024-3795(94)00205-3
author: J. Shen
published in: Linear Algebra and its Applications
publication date: 1996-10-07T00:00:00Z
review text: Let \(A\) be a nonnegative \(n\)-by-\(n\) matrix and let denote by \(\gamma(A)\) and \(D\) the exponent of primitivity and the diameter of the directed graph of \(A\), respectively. The author proves that \(\gamma (A) \leq D^2+1\) (a conjecture of R. E. Hartwig, M. Neumann and X. D. Lin (1984)).
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15A45
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 931937
zbMATH Keywords: nonnegative matrix
zbMATH Keywords: exponent of primitivity
zbMATH Keywords: directed graph
reviewed by: József Szilasi
MaRDI profile type: Publication
full work available at URL: 0024-3795(94)00205-3
OpenAlex ID: W2050052428
cites work: Bounds on the exponent of primitivity which depend on the spectrum and the minimal polynomial
cites work: Proof of a conjecture about the exponent of primitive matrices
cites work: Some estimated formulas for the Frobenius numbers
cites work: Bounds for a Linear Diophantine Problem of Frobenius
cites work: Note on Linear Forms
cites work: On a Problem of Partitions II
cites work: On the exponent of a primitive digraph
cites work: Q3475315
cites work: On small sumsets in an abelian group
cites work: Q5334400
description: scientific article; zbMATH DE number 931937