A stronger form of the Egorychev-Falikman theorem on permanents
type: Item
instance of: scholarly article
title: A stronger form of the Egorychev-Falikman theorem on permanents
zbMATH Open document ID: 0558.15009
DOI: 10.1016/0024-3795(84)90137-X
published in: Linear Algebra and its Applications
publication date: 1984-01-01T00:00:00Z
review text: Let A be an \(n\times n\) doubly stochastic matrix with columns \(a_ 1,...,a_ n\). Let \(A^{ij}\) be the matrix obtained from A by replacing each of the ith and the jth columns by \((a_ i+a_ j)\). Then at least one of the following conditions hold: (i) there exist i, j so that per \(A^{ij}<per A\), or (ii) if \(a_{ij}>0\) and \(a_{ik}>0\) then per \(A^{jk}\leq per A\). Furthermore if either A is partly decomposable or if \(A>0\) and some entry in A is not \(n^{-1}\), then (i) holds.
Mathematics Subject Classification ID: 15B51
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 15A45
zbMATH DE Number: 3889726
zbMATH Keywords: Egorychev-Falikman theorem
zbMATH Keywords: permanents
zbMATH Keywords: doubly stochastic matrix
zbMATH Keywords: van der Waerden conjecture
author: R. B. Bapat
reviewed by: Richard Sinkhorn
MaRDI profile type: Publication
cites work: Doubly stochastic matrices with equal subpermanents
cites work: The solution of van der Waerden's problem for permanents
cites work: Proof of the van der Waerden conjecture regarding the permanent of a doubly stochastic matrix
cites work: A Permanent Inequality
cites work: Subdefinite Matrices and Quadratic Forms
cites work: Permanents
cites work: Q3039497
cites work: Notes on Egoritsjev's proof of the van der Waerden conjecture
description: scientific article; zbMATH DE number 3889726