Combinatorial Matrix Classes

A thorough development of certain classes of matrices that have combinatorial definitions or significance.

Richard A. Brualdi (Author)

9780521865654, Cambridge University Press

Hardback, published 10 August 2006

554 pages, 4 tables
23.9 x 16.5 x 3.3 cm, 0.936 kg

'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

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.

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.

Subject Areas: Algebra [PBF]