Combinatorics of Nonnegative Matrices
About this Title
V. N. Sachkov, Steklov Institute of Mathematics, Moscow, Russia and V. E. Tarakanov, Steklov Institute of Mathematics, Moscow, Russia. Translated by Dr. Valentin F. Kolchin
Publication: Translations of Mathematical Monographs
Publication Year: 2002; Volume 213
ISBNs: 978-0-8218-2788-8 (print); 978-1-4704-4638-3 (online)
MathSciNet review: MR1905938
MSC: Primary 15-02; Secondary 15A48
In this book, 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. They also consider extremal problems related to matrices and problems where nonnegative matrices provide suitable investigative tools.
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, researchers, and engineers interested in combinatorics and its applications.
Graduate students, researchers, and engineers interested in combinatorics and its applications.
Table of Contents
- Matrices and Configurations
- Ryser classes
- Nonnegative matrices and extremal combinatorial problems
- Asymptotic methods in the study of nonnegative matrices
- Totally indecomposable, chainable, and prime matrices
- Sequences of nonnegative matrices