شمارش مسیرهای شبکه‌ای و کاربردها (احتمال و آمار ریاضی)

Probability and Mathematical Statistics: A Series of Monographs and Textbooks: Lattice Path Counting and Applications focuses on the principles, methodologies, and approaches involved in lattice path counting and applications, including vector representation, random walks, and rank order statistics. The book first underscores the simple and general boundaries of path counting. Topics include types of diagonal steps and a correspondence, paths within general boundaries, higher dimensional paths, vector representation, compositions, and domination, recurrence and generating function method, and reflection principle. The text then examines invariance and fluctuation and random walk and rank order statistics. Discussions focus on random walks, rank order statistics, Chung-Feller theorems, and Sparre Andersen's equivalence. The manuscript takes a look at convolution identities and inverse relations and discrete distributions, queues, trees, and search codes, as well as discrete distributions and a correlated random walk, trees and search codes, convolution identities, and orthogonal relations and inversion formulas. The text is a valuable reference for mathematicians and researchers interested in in lattice path counting and applications. Content: Front Matter, Page iii Copyright, Page iv Dedication, Page v Inside Front Cover, Page vi Preface, Pages ix-x Acknowledgments, Page xi 1 - Path Counting—Simple Boundaries, Pages 1-29 2 - Path Counting—General Boundaries, Pages 31-61 3 - Invariance and Fluctuation, Pages 63-83 4 - Random Walk and Rank Order Statistics, Pages 85-125 5 - Discrete Distributions, Queues, Trees, and Search Codes, Pages 127-164 6 - Convolution Identities and Inverse Relations, Pages 165-181 Index, Pages 183-185 Probability and Mathematical Statistics: A Series of Monographs and Textbooks, Pages ibc1-ibc2 Path Counting--simple Boundaries -- Path Counting--general Boundaries -- Invariance And Fluctuation -- Random Walk And Rank Order Statistics -- Discrete Distributions, Queues, Trees, And Search Codes -- Convolution Identities And Inverse Relations. Sri Gopal Mohanty. Includes Bibliographies And Index.