Combinatorics of Nonnegative Matrices

Description

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