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Combinatorics of Nonnegative Matrices
 
V. N. Sachkov Steklov Institute of Mathematics, Moscow, Russia
V. E. Tarakanov Steklov Institute of Mathematics, Moscow, Russia
Combinatorics of Nonnegative Matrices
Hardcover ISBN:  978-0-8218-2788-8
Product Code:  MMONO/213
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-4638-3
Product Code:  MMONO/213.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Hardcover ISBN:  978-0-8218-2788-8
eBook: ISBN:  978-1-4704-4638-3
Product Code:  MMONO/213.B
List Price: $320.00 $242.50
MAA Member Price: $288.00 $218.25
AMS Member Price: $256.00 $194.00
Combinatorics of Nonnegative Matrices
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Combinatorics of Nonnegative Matrices
V. N. Sachkov Steklov Institute of Mathematics, Moscow, Russia
V. E. Tarakanov Steklov Institute of Mathematics, Moscow, Russia
Hardcover ISBN:  978-0-8218-2788-8
Product Code:  MMONO/213
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-4638-3
Product Code:  MMONO/213.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Hardcover ISBN:  978-0-8218-2788-8
eBook ISBN:  978-1-4704-4638-3
Product Code:  MMONO/213.B
List Price: $320.00 $242.50
MAA Member Price: $288.00 $218.25
AMS Member Price: $256.00 $194.00
  • Book Details
     
     
    Translations of Mathematical Monographs
    Volume: 2132002; 269 pp
    MSC: Primary 05; Secondary 15; 93;

    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.

    Readership

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

  • Table of Contents
     
     
    • Chapters
    • 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
  • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2132002; 269 pp
MSC: Primary 05; Secondary 15; 93;

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.

Readership

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

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

    Zentralblatt MATH
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.