Enumerative Combinatorics

Charalambos A. Charalambides

626 pages, parution le 28/11/2002

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Résumé

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.

Clarifies each definition and theorem with remarks that also point out useful extensions or generalizations of the concepts or results
Focuses on counting configurations that satisfy a variety of specified conditions
Includes a chapter that briefly introduces the notion of probability and its connection to counting configurations
Offers practical exercises of varying difficulty at the end of each chapter and provides hints to their solutions in an appendix

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

L'auteur - Charalambos A. Charalambides

Charalambos A. Charalambides, PHD, is a Professor in the Department of Mathematics, University of Athens, Greece. He is Associate Editor of Communications in Statistics, author of Enumerative Combinatorics, and an elected member of the International Statistical Institute.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Chapman and Hall / CRC
Auteur(s)	Charalambos A. Charalambides
Parution	28/11/2002
Nb. de pages	626
Format	16 x 24
Couverture	Relié
Poids	1011g
Intérieur	Noir et Blanc
EAN13	9781584882909
ISBN13	978-1-58488-290-9