Determining the Schein Rank of Boolean Matrices

In this paper we present some results of Schein rank of Boolean matrices. A notion of the intersection number of a bipartite graph is defined and its applications to Schein rank of Boolean matrices are derived. We discuss minimal and maximal matrices of given Schein rank, the number of m × n Boolean...

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Bibliographic Details
Published inMatrix Methods: Theory, Algorithms And Applications pp. 85 - 103
Main Author Marenich, Evgeny E.
Format Book Chapter
LanguageEnglish
Published WORLD SCIENTIFIC 01.04.2010
Subjects
Algebra and Matrices
Boolean matrix
coding functions for bipartite graphs
Schein rank
Online AccessGet full text
ISBN9812836020
9789812836014
9812836012
9814469556
9789812836021
9789814469555
DOI10.1142/9789812836021_0005

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Summary:In this paper we present some results of Schein rank of Boolean matrices. A notion of the intersection number of a bipartite graph is defined and its applications to Schein rank of Boolean matrices are derived. We discuss minimal and maximal matrices of given Schein rank, the number of m × n Boolean matrices with given Schein rank. The Schein ranks of some m × n Boolean matrices are determined. In the last section, we give some further result concerning the Schein rank of Boolean matrices.
ISBN:9812836020
9789812836014
9812836012
9814469556
9789812836021
9789814469555
DOI:10.1142/9789812836021_0005