Lattice Path Counting and Applications

PrefaceAcknowledgements1. 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 References2. Path Counting—General Boundaries 1. Introduction 2. Paths within General Boundaries 3. Some Generalizations 4. Higher Dimensional Paths 5. Types of Diagonal Steps and a Correspondence 6. Concluding Remarks Exercises References3. Invariance and Fluctuation 1. Introduction 2. Takacs' Urn Problem 3. Chung-Feller Theorems 4. Sparre Andersen's Equivalence 5. Concluding Remarks Exercises References4. 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 References5. Discrete Distributions, Queues, Trees, and Search Codes 1. Introduction 2. Discrete Distributions and a Correlated Random Walk 3. Queues 4. Trees and Search Codes 5. Concluding Remarks Exercises References6. Convolution Identities and Inverse Relations 1. Introduction 2. Convolution Identities 3. Orthogonal Relations and Inversion Formulas 4. Concluding Remarks Exercises ReferencesIndex