Charalambos A. Charalambides - Böcker

Enumerative Combinatorics presents elaborate and systematic coverage of the theory of enumeration. The first seven chapters provide the necessary background, including basic counting principles and techniques, elementary enumerative topics, and an extended presentation of generating functions and recurrence relations. The remaining seven chapters focus on more advanced topics, including, Stirling numbers, partitions of integers, partition polynomials, Eulerian numbers and Polya's counting theorem.Extensively classroom tested, this text was designed for introductory- and intermediate-level courses in enumerative combinatorics, but the far-reaching applications of the subject also make the book useful to those in operational research, the physical and social science, and anyone who uses combinatorial methods. Remarks, discussions, tables, and numerous examples support the text, and a wealth of exercises-with hints and answers provided in an appendix--further illustrate the subject's concepts, theorems, and applications.

A unique approach illustrating discrete distribution theory through combinatorial methods This book provides a unique approach by presenting combinatorial methods in tandem with discrete distribution theory. This method, particular to discreteness, allows readers to gain a deeper understanding of theory by using applications to solve problems. The author makes extensive use of the reduction approach to conditional distributions of independent random occupancy numbers, and provides excellent studies of occupancy and sequential occupancy distributions, convolutions of truncated discrete distributions, and compound and mixture distributions.Combinatorial Methods in Discrete Distributions begins with a brief presentation of set theory followed by basic counting principles. Fundamental principles of combinatorics, finite differences, and discrete probability are included to give readers the necessary foundation to the topics presented in the text.A thorough examination of the field is provided and features: Stirling numbers and generalized factorial coefficientsOccupancy and sequential occupancy distributionsn-fold convolutions of truncated distributionsCompound and mixture distributionsThoroughly worked examples aid readers in understanding complex theory and discovering how theory can be applied to solve practical problems. An appendix with hints and answers to the exercises helps readers work through the more complex sections. Reference notes are provided at the end of each chapter, and an extensive bibliography offers readers a resource for additional information on specialized topics.

A self-contained study of the various applications and developments of discrete distribution theoryWritten by a well-known researcher in the field, Discrete q-Distributions features an organized presentation of discrete q-distributions based on the stochastic model of a sequence of independent Bernoulli trials. In an effort to keep the book self-contained, the author covers all of the necessary basic q-sequences and q-functions.The book begins with an introduction of the notions of a q-power, a q-factorial, and a q-binomial coefficient and proceeds to discuss the basic q-combinatorics and q-hypergeometric series. Next, the book addresses discrete q-distributions with success probability at a trial varying geometrically, with rate q, either with the number of previous trials or with the number of previous successes. Further, the book examines two interesting stochastic models with success probability at any trial varying geometrically both with the number of trials and the number of successes and presents local and global limit theorems. Discrete q-Distributions also features: Discussions of the definitions and theorems that highlight key concepts and resultsSeveral worked examples that illustrate the applications of the presented theoryNumerous exercises at varying levels of difficulty that consolidate the concepts and results as well as complement, extend, or generalize the resultsDetailed hints and answers to all the exercises in an appendix to help less-experienced readers gain a better understanding of the contentAn up-to-date bibliography that includes the latest trends and advances in the field and provides a collective source for further researchAn Instructor’s Solutions Manual available on a companion websiteA unique reference for researchers and practitioners in statistics, mathematics, physics, engineering, and other applied sciences, Discrete q-Distributions is also an appropriate textbook for graduate-level courses in discrete statistical distributions, distribution theory, and combinatorics.

Enumerative Combinatorics presents elaborate and systematic coverage of the theory of enumeration. The first seven chapters provide the necessary background, including basic counting principles and techniques, elementary enumerative topics, and an extended presentation of generating functions and recurrence relations. The remaining seven chapters focus on more advanced topics, including, Stirling numbers, partitions of integers, partition polynomials, Eulerian numbers and Polya's counting theorem.Extensively classroom tested, this text was designed for introductory- and intermediate-level courses in enumerative combinatorics, but the far-reaching applications of the subject also make the book useful to those in operational research, the physical and social science, and anyone who uses combinatorial methods. Remarks, discussions, tables, and numerous examples support the text, and a wealth of exercises-with hints and answers provided in an appendix--further illustrate the subject's concepts, theorems, and applications.

This book is devoted to the study of multivariate discrete q-distributions, which is greatly facilitated by existing multivariate q-sequences and q-functions.