Front Cover; Lattice Path Counting and Applications; Copyright Page; Dedication; Table of Contents; Preface; Acknowledgments; Chapter 1. Path Counting-Simple Boundaries; 1. Introduction; 2. Two-Dimensional Lattice Paths; 3. Reflection Principle (Conjugation); 4. Method of Penetrating Analysis; 5. Recurrence and Generating Function Method; 6. Vector Representation, Compositions, and Domination; 7. Diagonal Steps; 8. Summary and Concluding Remarks; Exercises; References; Chapter 2. Path Counting-General Boundaries ; 1. Introduction; 2. Paths within General Boundaries; 3. Some Generalizations

4. Higher Dimensional Paths5. Types of Diagonal Steps and a Correspondence; 6. Concluding Remarks; Exercises; References; Chapter 3. Invariance and Fluctuation; 1. Introduction; 2. Takács' Urn Problem; 3. Chung-Feller Theorems; 4. Sparre Andersen's Equivalence; 5. Concluding Remarks; Exercises; References; Chapter 4. Random Walk and Rank Order Statistics; 1. Introduction; 2. Random Walks; 3. Rank Order Statistics-Gnedenko's Technique; 4. Rank Order Statistics-The Dwass Technique; 5. Concluding Remarks; Exercises; References; Chapter 5. Discrete Distributions, Queues, Trees, and Search Codes

1. Introduction2. Discrete Distributions and a Correlated Random Walk; 3. Queues; 4. Trees and Search Codes; 5. Concluding Remarks; Exercises; References; Chapter 6. Convolution Identities and Inverse Relations; 1. Introduction; 2. Convolution Identities; 3. Orthogonal Relations and Inversion Formulas; 4. Concluding Remarks; Exercises; References; Index; Probability and Mathematical Statistics