On a conjecture of R. A. Brualdi
type: Item
instance of: scholarly article
title: On a conjecture of R. A. Brualdi
zbMATH Open document ID: 0625.15014
DOI: 10.1016/0024-3795(87)90078-4
published in: Linear Algebra and its Applications
publication date: 1987-01-01T00:00:00Z
review text: Let \(n>2\). Let \(X_ n=(x_{ij})\) denote the \(n\times n\) matrix that has \(x_{ij}=(n-1)/n(n-2)\) if \(i\neq j\), \(x_{ij}=0\) if \(i=j\), \(i,j=1,...,n- 1\); \(x_{ij}=1/n\) if either i or j equals n. The author refutes a conjecture of \textit{R. A. Brualdi} [Linear Multilinear Algebra 17, 5-18 (1985; Zbl 0564.15010)] that \(X_ n\) has the unique minimal permanent among all \(n\times n\) doubly stochastic matrices with zeros in positions (i,i), \(i=1,...,n-1\), for \(n\geq 5\). The minimum permanent is determined for a subset of such doubly stochastic matrices.
Mathematics Subject Classification ID: 15B51
Mathematics Subject Classification ID: 15A15
zbMATH DE Number: 4014912
zbMATH Keywords: unique minimal permanent
zbMATH Keywords: doubly stochastic matrices
Wikidata QID: Q123180128
reviewed by: Richard Sinkhorn
MaRDI profile type: Publication
full work available at URL: 0024-3795(87)90078-4
OpenAlex ID: W1999198595
cites work: An interesting face of the polytope of doubly stochastic matrices
cites work: Minimum permanents of doubly stochastic matrices with prescribed zero entries†
author: Henryk Minc
description: scientific article; zbMATH DE number 4014912