Charalambides, Charalambos A.

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.

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.