Combinatorial enumeration is a readily accessible subject full of easily stated, but sometimes tantalizingly difficult problems. This book leads the reader in a leisurely way from the basic notions to a variety of topics, ranging from algebra to statistical physics. Its aim is to introduce the student to a fascinating field, and to be a source of information for the professional mathematician who wants to learn more about the subject. The book is organized in three parts: Basics, Methods, and Topics. There are 666 exercises, and as a special feature every chapter ends with a highlight, discussing a particularly beautiful or famous result.
Author(s): Martin Aigner (auth.)
Series: Graduate Texts in Mathematics 238
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2007
Language: English
Pages: 565
Tags: Combinatorics; Mathematical and Computational Physics; Discrete Mathematics in Computer Science
Front Matter....Pages I-X
Introduction....Pages 1-2
Front Matter....Pages 3-3
Fundamental Coefficients....Pages 5-52
Formal Series and Infinite Matrices....Pages 53-90
Front Matter....Pages 91-91
Generating Functions....Pages 93-141
Hypergeometric Summation....Pages 143-178
Sieve Methods....Pages 179-238
Enumeration of Patterns....Pages 239-285
Front Matter....Pages 287-287
The Catalan Connection....Pages 289-344
Symmetric Functions....Pages 345-392
Counting Polynomials....Pages 393-450
Models from Statistical Physics....Pages 451-518
Back Matter....Pages 519-565
