A note on a conjecture on permanents
type: Item
instance of: scholarly article
title: A note on a conjecture on permanents
zbMATH Open document ID: 0589.15016
DOI: 10.1016/0024-3795(86)90212-0
published in: Linear Algebra and its Applications
publication date: 1986-01-01T00:00:00Z
review text: The author considers the problem of determining the maximum of the function \[ \psi (X)=\prod^{n}_{i=1}\sum^{n}_{j=1}x_{ij}+\prod^{n}_{j=1}\sum\;sp{n}_{\quad i=1}x_{ij}-per X \] for all nonnegative \(n\times n\) matrices \(X=(x_{ij})\), the sum of whose entries is n. Conditions are given for which the maximum occurs at \(X=J_ n\), the \(n\times n\) matrix whose entries all equal \(n^{-1}\). Some general bounds are given for the row and column sums of a maximizing matrix X.
Mathematics Subject Classification ID: 15B51
Mathematics Subject Classification ID: 15A15
zbMATH DE Number: 3946365
zbMATH Keywords: doubly stochastic matrix
zbMATH Keywords: permanent
zbMATH Keywords: maximizing matrix
Wikidata QID: Q123357765
author: Suk-Geun Hwang
reviewed by: Richard Sinkhorn
MaRDI profile type: Publication
full work available at URL: 0024-3795(86)90212-0
OpenAlex ID: W1991197089
cites work: Q5672631
cites work: Theory of permanents 1978–1981
cites work: Q4184984
cites work: A problem related to the van der waerden permanent theorem*
description: scientific article; zbMATH DE number 3946365