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Enumerative Combinatorics provides systematic coverage of the theory of enumeration. The author first lays a foundation with basic counting principles and techniques and elementary classical enumerative topics, then proceeds to more advanced topics, including the partition polynomials, Stirling numbers, and the Eulerian numbers of generalized binomials. The text is supported by remarks and discussions, numerous tables, exercises, and a wealth of examples that illustrate the concepts, theorems, and applications of the subject. Designed to serve as a text for upper-level and graduate students, this book will be useful and enlightening to anyone who uses combinatorial methods.
List of contents
Basic Counting Principles. Permutations and Combinations. Factorials, Binomial and Multinomial Coefficients. The Principle of Inclusion and Exclusion.Permutations with Fixed Points and Successions. Generating Functions. Recurrence Relations. Stirling Numbers. Distributions and Occupancy. Partitions of Integers. Partition Polynomials. Cycles of Permutations. Equivalence Classes.Runs of Permutations and Eulerian Numbers. Hints and Answers to Exercises. Bibliography. Index.
About the author
Charalambides, Charalambos A.
Summary
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.
