Combinatorial Matrix Classes
Edition: 1 edition
Publisher: Cambridge University Press
Published: August 28, 2006
Language: eng
Format: Hardcover
Number of pages: 554
ISBN-13: 9780521865654
Subjects: Algebra; Mathematics; Science/Mathematics; Algebra - General; Matrices; Mathematics / Algebra / General
First sentence: In this chapter we introduce some concepts and theorems that are important for the rest of this book.
Description: 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.
Notes: Encyclopedia of Mathematics and its Applications