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Combinatorial Matrix Classes

Part of Encyclopedia of Mathematics and its Applications

Author: Richard A. Brualdi, University of Wisconsin, Madison

Date Published: August 2006
availability: Available
format: Hardback
isbn: 9780521865654

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About the Authors

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.
- Thorough and complete development of some important matrix classes of combinatorial importance
- Both existence questions and algorithms are given for most matrix classes treated
- Important combinatorial and linear-algebraic parameters associated with these classes are thoroughly investigated
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'The treatment is clearly explained, methodical and accurate and includes details of many important algorithms as well as proofs of many important theorems, although some proofs are necessarily omitted … the test is well cross-referenced and thoughtfully written, meaning that it is very accessible. All in all, a treasure trove of results written by an acknowledged master of combinatorial matrix theory.' Zentralblatt MATH

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Product details
- Date Published: August 2006
- format: Hardback
- isbn: 9780521865654
- length: 554 pages
- dimensions: 239 x 165 x 33 mm
- weight: 0.936kg
- contains: 4 tables
- availability: Available
Table of Contents
1. Introduction
2. Basic existence theorems for matrices with prescribed properties
3. The class A(R
S) of (0,1)-matrices
4. More on the class A(R
S) of (0,1)-matrices
5. The class T(R) of tournament matrices
6. Interchange graphs
7. Classes of symmetric integral matrices
8. Convex polytopes of matrices
9. Doubly stochastic matrices.
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Author
Richard A. Brualdi, University of Wisconsin, Madison
Richard A. Brualdi is UWF Beckwith Bascom Professor of Mathematics at the University of Wisconsin, Madison.