A graph theoretic upper bound on the permanent of a nonnegative integer matrix. I
type: Item
instance of: scholarly article
title: A graph theoretic upper bound on the permanent of a nonnegative integer matrix. I
zbMATH Open document ID: 0551.15005
DOI: 10.1016/0024-3795(84)90030-2
author: N. E. Zubov
published in: Linear Algebra and its Applications
publication date: 1984-01-01T00:00:00Z
review text: If A is a fully indecomposable \(n\times n\) matrix with nonnegative integer entries which has row and column \(r_ i\) and \(c_ i\), respectively, then \(per A\leq 1+\min [\prod_{i}(r_ i-1),\quad \prod_{i}(c_ i-1)].\)
Mathematics Subject Classification ID: 15B36
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 3877357
zbMATH Keywords: permanent
zbMATH Keywords: nonnegative integer matrix
zbMATH Keywords: multigraph
zbMATH Keywords: fully indecomposable
reviewed by: Richard Sinkhorn
MaRDI profile type: Publication
full work available at URL: 0024-3795(84)90030-2
OpenAlex ID: W1995854161
cites work: Q4044717
cites work: Convex polyhedra of doubly stochastic matrices. I: Applications of the permanent function
cites work: The diagonal equivalence of a nonnegative matrix to a stochastic matrix
cites work: A graph theoretic upper bound on the permanent of a nonnegative integer matrix. II. The extremal case
cites work: Two Algorithms for Bipartite Graphs
cites work: An Upper Bound for the Permanent of a Fully Indecomposable Matrix
cites work: Q4111023
cites work: A Decomposition Methodology and a Class of Algorithms for the Solution of Nonlinear Equations
cites work: Upper bounds for permanents of $\left( {0,\,1} \right)$-matrices
cites work: A graph theoretical interpretation of nonsymmetric permutation on sparse matrices
description: scientific article; zbMATH DE number 3877357