Matrices and set differences
type: Item
instance of: scholarly article
title: Matrices and set differences
zbMATH Open document ID: 0534.05018
DOI: 10.1016/0012-365X(84)90114-6
published in: Discrete Mathematics
publication date: 1984-01-01T00:00:00Z
review text: Let A and B be (0,1)-matrices of sizes m by t and t by n, respectively. Let \(x_ 1,...,x_ t\) denote t independent indeterminates over the rational field Q and define \(X=diag[x_ 1,...,x_ t]\). We study the matrix equation \(AXB=Y\). We first discuss its combinatorial significance relative to topics such as set intersections and the Marica-Schönheim theorem on set differences. We then prove the following theorem concerning the matrix Y. Suppose that the matrix Y of size m by n has rank m. Then Y contains m distinct nonzero elements, one in each of the m rows of Y.
Mathematics Subject Classification ID: 05B20
Mathematics Subject Classification ID: 15B36
zbMATH DE Number: 3847406
zbMATH Keywords: (0,1)-matrix
zbMATH Keywords: indeterminates
zbMATH Keywords: set intersections
zbMATH Keywords: set differences
MaRDI profile type: Publication
cites work: The Number of values of Combinatorial Functions
cites work: Properties of (0,1)-matrices with no triangles
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author: Herbert John Ryser
description: scientific article; zbMATH DE number 3847406