Alternating sign matrices
type: Item
instance of: scholarly article
title: Alternating sign matrices
zbMATH Open document ID: 0826.05014
DOI: 10.1016/0012-365X(94)00125-3
author: Mireille Bousquet-Mélou
author: Laurent Habsieger
published in: Discrete Mathematics
publication date: 1995-11-26T00:00:00Z
review text: An alternating sign matrix \(A= (A_{ij})_{1\leq i,j\leq n}\) is an \(n\times n\)-matrix with entries \(\{0, 1, -1\}\), such that in each row and in each column the elements equal to 1 and \(-1\) alternate (if you do not consider the zeros) and the sum of the entries of each row and each column is 1. The authors establish a bijection between the set of the alternating sign matrices of type \(n\times n\) and the set of the \(n\times n\) matrices of type \(\mathcal P\). Then they study the symmetries presented by the alternating sign matrices. By generalizing the matrices of type \(\mathcal P\), one can compute the number of matrices having some symmetries and it is sufficient to consider this kind of matrices in coding theory. An application of these matrices to obtain the configurations of paths of length \(n\) is given in the end of the paper, together with computations for some particular cases.
Mathematics Subject Classification ID: 05B20
Mathematics Subject Classification ID: 15B36
zbMATH DE Number: 773902
zbMATH Keywords: alternating sign matrix
zbMATH Keywords: symmetries
reviewed by: Mirela Ştefănescu
describes a project that uses: ROBBINS
MaRDI profile type: Publication
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full work available at URL: 0012-365x(94)00125-3
OpenAlex ID: W2410308809
description: scientific article; zbMATH DE number 773902