**Translations of Mathematical Monographs**

2002;
269 pp;
Hardcover

MSC: Primary 05;
Secondary 15; 93

**Print ISBN: 978-0-8218-2788-8
Product Code: MMONO/213**

List Price: $115.00

Individual Member Price: $92.00

# Combinatorics of Nonnegative Matrices

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*V. N. Sachkov; V. E. Tarakanov*

The variety of combinatorial properties of nonnegative matrices is widely
discussed in the mathematical literature, and there are many papers on this
topic. However, there are few monographs devoted to these properties of
nonnegative matrices. This book fills that gap and presents a summary of the
existing material. It provides a good entry point into the subject and includes
exercises to aid students.

The authors focus on the relation of matrices with nonnegative elements to
various mathematical structures studied in combinatorics. In addition to
applications in graph theory, Markov chains, tournaments, and abstract
automata, the authors consider relations between nonnegative matrices and
structures such as coverings and minimal coverings of sets by families of
subsets. They also give considerable attention to the study of various
properties of matrices and to the classes formed by matrices with a given
structure.

The authors discuss enumerative problems using both combinatorial and
probabilistic methods. It also considers extremal problems related to matrices
and problems where nonnegative matrices provide suitable investigative
tools.

This book was developed for the most part as a theoretical research text,
keeping in mind applications of nonnegative matrices. Among the applications,
the most significant included are in the theory of Markov chains, in linear
programming for constructing and analyzing economic models, and in information
theory for designing reliable information devices. The book is suitable for
specialists in these areas of engineering and the applied sciences.

The book contains some classical theorems and a significant number of results
not previously published in monograph form, including results obtained by the
authors in the last few years. It is appropriate for graduate students and
researchers interested in combinatorics and its applications.

#### Table of Contents

# Table of Contents

## Combinatorics of Nonnegative Matrices

#### Readership

Graduate students, researchers, and engineers interested in combinatorics and its applications.

#### Reviews

The exposition is generally elementary and clear … For a course in combinatorics with emphasis on matrix methods, the book is quite suitable.

-- Zentralblatt MATH