Combinatorics of Nonnegative Matrices

✍ Scribed by V. N. Sachkov, V. E. Tarakanov

• Publisher: AMS
• Year: 2002
• Tongue: English
• Leaves: 276
• Category: Library

✦ Table of Contents

Title page
Preface
List of Notation
Chapter 1. Matrices and Configurations
Introduction
1.1. Definitions and examples
1.2. Term rank. Arrangement of positive elements
1.3. Combinatorial theory of cyclic matrices
Chapter 2. Ryser Classes
Introduction
2.1. A constructive description of Ryser classes
2.2. Invariant sets
2.3. Estimates of the term rank
Chapter 3. Nonnegative Matrices and Extremal Combinatorial Problems
Introduction
3.1. Forbidden configurations
3.2. Covering problem
3.3. The van der Waerden-Egorychev-Falikman Theorem
Chapter 4. Asymptotic Methods in the Study of Nonnegative Matrices
Introduction
4.1. Nonnegative matrices and graphs
4.2. Asymptotics of the number of primitive (0,l)-matrices
4.3. Asymptotics of the permanent of a random (0,l)-matrix
4.4. Random lattices and Boolean algebras
4.5. Coverings of sets and (0,l)-matrices
4.6. Random coverings of sets
Chapter 5. Totally Indecomposable, Chainable, and Prime Matrices
Introduction
5.1. Totally indecomposable and chainable matrices
5.2. Rectangular nonnegative matrices
5.3. Rectangular nonnegative chainable matrices
5.4. Extension of partial diagonals
5.5. Prime Boolean matrices
5.6. Prime nonnegative matrices
Chapter 6. Sequences of Nonnegative Matrices
Introduction
6.1. Directed graphs of nonnegative matrices
6.2. Irreducible and primitive matrices
6.3. Tournament matrices
6.4. Associated operator
6.5. Sequences of powers of a nonnegative matrix
6.6. Ergodicity of sequences of nonnegative matrices
Bibliography
Index