Combinatorial Matrix Classes, Volume 13

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Cambridge University Press, Aug 10, 2006 - Mathematics - 544 pages
A natural sequel to the author's previous book Combinatorial Matrix Theory written with H. J. Ryser, this is the first book devoted exclusively to existence questions, constructive algorithms, enumeration questions, and other properties concerning classes of matrices of combinatorial significance. Several classes of matrices are thoroughly developed including the classes of matrices of 0's and 1's with a specified number of 1's in each row and column (equivalently, bipartite graphs with a specified degree sequence), symmetric matrices in such classes (equivalently, graphs with a specified degree sequence), tournament matrices with a specified number of 1's in each row (equivalently, tournaments with a specified score sequence), nonnegative matrices with specified row and column sums, and doubly stochastic matrices. Most of this material is presented for the first time in book format and the chapter on doubly stochastic matrices provides the most complete development of the topic to date.

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Preface page ix
Basic Existence Theorems for Matrices with
3TheClassARS of 01Matrices
More on the Class ARS of 01Matrices
5TheClassT R of Tournament Matrices
Interchange Graphs
Classes of Symmetric Integral Matrices
Convex Polytopes of Matrices
Doubly Stochastic Matrices
Master Bibliography 511

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About the author (2006)

Richard A. Brualdi is UWF Beckwith Bascom Professor of Mathematics at the University of Wisconsin, Madison.

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