Synopses & Reviews
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.
Synopsis
The first book devoted exclusively to existence questions, constructive algorithms, enumeration questions, and other properties concerning classes of matrices of combinatorial significance. Combinatorial Matrix Classes is a natural sequel to the author's previous book Combinatorial Matrix Theory written with H. J. Ryser, and is likely to achieve similar classic status.
Synopsis
Combinatorial Matrix Classes is the first book devoted exclusively to existence questions, constructive algorithms, enumeration questions, and other properties concerning classes of matrices of combinatorial significance. It is a natural sequel to the author's previous book Combinatorial Matrix Theory, written with H. J. Ryser, which has become the standard reference work in the field. Most of the 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.
Synopsis
A thorough development of certain classes of matrices that have combinatorial definitions or significance.
Synopsis
Steven Finch provides 136 essays, each devoted to a mathematical constant or a class of constants, from the well known to the highly exotic. This book is helpful both to readers seeking information about a specific constant, and to readers who desire a panoramic view of all constants coming from a particular field, for example, combinatorial enumeration or geometric optimization. Unsolved problems appear virtually everywhere as well. This work represents an outstanding scholarly attempt to bring together all significant mathematical constants in one place.
About the Author
Richard A. Brualdi is UWF Beckwith Bascom Professor of Mathematics at the University of Wisconsin, Madison.
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.