Maximum permanents of matrices of zeros and ones
type: Item
instance of: scholarly article
title: Maximum permanents of matrices of zeros and ones
zbMATH Open document ID: 0647.15002
DOI: 10.1016/0097-3165(88)90019-2
author: Richard A. Brualdi
author: John Goldwasser
author: T. S. Michael
published in: Journal of Combinatorial Theory. Series A
publication date: 1988-01-01T00:00:00Z
review text: Let A be a 0,1-matrix of order n with t zeros. The main results of this paper are contained in three theorems. The first establishes an upper bound on per(A) as a function of n and t. The second obtains the least upper bound on per(A) and characterizes the matrices that realize it, for \(n\geq 3\) and n 2-2n\(\leq t\leq n\) 2-n. (Note: per A\(=0\) if \(t>n\) 2-n.) The third characterizes the matrices that achieve the least upper bound on per(A), for \(n\geq 3\) and \(0\leq t\leq 2n\). The proofs rely heavily on partitioned matrices.
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 15A45
Mathematics Subject Classification ID: 05B20
zbMATH DE Number: 4055780
zbMATH Keywords: maximum permanents
zbMATH Keywords: permanent
zbMATH Keywords: 0,1-matrix
zbMATH Keywords: upper bound
MaRDI profile type: Publication
full work available at URL: 0097-3165(88)90019-2
OpenAlex ID: W1985359679
cites work: Q4044717
cites work: Matrix factorizations of determinants and permanents
cites work: Upper bounds for permanents of $\left( {0,\,1} \right)$-matrices
cites work: Permanents
cites work: Q3243274
cites work: Matrices of zeros and ones
cites work: Q3851094
description: scientific article; zbMATH DE number 4055780