A graph theoretic upper bound on the permanent of a nonnegative integer matrix. II. The extremal case
type: Item
instance of: scholarly article
title: A graph theoretic upper bound on the permanent of a nonnegative integer matrix. II. The extremal case
zbMATH Open document ID: 0551.15006
DOI: 10.1016/0024-3795(84)90031-4
author: N. E. Zubov
published in: Linear Algebra and its Applications
publication date: 1984-01-01T00:00:00Z
review text: [For part I see ibid. 61, 187-198 (1984; reviewed above)]. Let A be a fully indecomposable \(n\times n\) matrix with integer entries and row and column sums \(r_ i\) and \(c_ i\), respectively. Matrices A are characterized for which per A\(=1+\min [\prod_{i}(r_ i- 1),\prod_{i}(c_ i-1)]\) holds.
Mathematics Subject Classification ID: 15B36
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 3877358
zbMATH Keywords: multigraphs
zbMATH Keywords: permanent
zbMATH Keywords: nonnegative integer matrix
zbMATH Keywords: fully indecomposable
reviewed by: Richard Sinkhorn
MaRDI profile type: Publication
full work available at URL: 0024-3795(84)90031-4
OpenAlex ID: W1998844561
cites work: Convex polyhedra of doubly stochastic matrices. I: Applications of the permanent function
cites work: A graph theoretic upper bound on the permanent of a nonnegative integer matrix. I
cites work: A Simplified Form for Nearly Reducible and Nearly Decomposable Matrices
cites work: A graph theoretical interpretation of nonsymmetric permutation on sparse matrices
cites work: Problems Involving Diagonal Products in Nonnegative Matrices
description: scientific article; zbMATH DE number 3877358