Combinatorial Matrix Classes
Combinatorial Matrix Classes
$205.00
USDA 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
Reviews & endorsements
"Enormous fun, and you don't even have to follow any difficult arguments; a treasure-trove for the mathematical beachcomber."
The Mathematical Gazette
"I think all mathematicians should own this book...there are sections where the author conveys admirably his excitement over some unexpected and beautiful sequence of ideas. I pay the author the earnest compliment of stating that nearly every page in the book is an adventure."
The Mathematical Intelligencer
"Very accessible...The author's clear and engaging style makes the book a pleasure to read."
MAA Reviews
"This is a very useful book...The emphasis is on the mathematical origin of the constants and their interrelationships. The aim is always to be clear and complete, to motivate why a particular constant or idea is important, and to indicate exactly where in the literature one should look for rigorous proofs and further elaboration. This book should be in each mathematical library."
Monatshefte für Mathematik
"I consider this book to be an essential component of all mathematical libraries. I have placed it on my 'within the grasp' shelf and have strongly recommended to the college library that it be added to the reference collection."
Charles Ashbacher, amazon.com
"The present book fully lives up to all expectations... it presents much material that was not before available in book form, and also gathers together related but previously scattered material... Readers are likely to enjoy this encyclopedic format even if not all of the subtopics are of immediate interest."
Thomas Britz, Mathematical Reviews
Product details
August 2006Hardback
9780521865654
554 pages
239 × 165 × 33 mm
0.936kg
4 tables
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.
