A Course in Enumeration (Graduate Texts in Mathematics)

Aigner, Martin

Springer（2010/11発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 575 p.
• 言語 ENG
• 商品コード 9783642072536
• DDC分類 511

Full Description

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.

Contents

Basics.- Fundamental Coefficients.- Formal Series and Infinite Matrices.- Methods.- Generating Functions.- Hypergeometric Summation.- Sieve Methods.- Enumeration of Patterns.- Topics.- The Catalan Connection.- Symmetric Functions.- Counting Polynomials.- Models from Statistical Physics.