Balancing matrices with line shifts
type: Item
instance of: scholarly article
title: Balancing matrices with line shifts
zbMATH Open document ID: 0542.05015
DOI: 10.1007/BF02579185
published in: Combinatorica
publication date: 1983-01-01T00:00:00Z
review text: The authors give a deterministic proof [not a probabilistic one as in the original paper written by \textit{J. Komlós} and \textit{M. Suliok}, Comb. Theory Appl., Colloquia Math. Soc. János Bolyai 4, 721-728 (1970; Zbl 0216.020)] of the following theorem: If \(A=(a_{ij})\), with \(a_{ij}=\pm 1\) is a \(n\times n\) matrix, then it is possible to multiply some rows and columns by -1 such that the absolute value of the sum of the elements of the matrix is \(\leq 2\), if n is even and 1 if n is odd.
Mathematics Subject Classification ID: 05B20
zbMATH DE Number: 3861175
zbMATH Keywords: row and column sums
zbMATH Keywords: (1,-1)-matrices
zbMATH Keywords: deterministic proof
author: József Beck
author: Joel Spencer
reviewed by: Mirela Ştefănescu
MaRDI profile type: Publication
cites work: Minimization of ±1 matrices under line shifts
cites work: ``Integer-making'' theorems
full work available at URL: https://doi.org/10.1007/bf02579185
OpenAlex ID: W4240009950
description: scientific article; zbMATH DE number 3861175