A Course in Enumeration

2007
ISBN: 978-3-540-39032-9
Verlag: Springer

Buch, Englisch, 566 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1021 g

Reihe: Graduate Texts in Mathematics

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 basic notions of combinatorial enumeration to a variety of topics, ranging from algebra to statistical physics. The book is organized in three parts: Basics, Methods, and Topics. The aim is to introduce readers to a fascinating field, and to offer a sophisticated source of information for professional mathematicians desiring to learn more. There are 666 exercises, and every chapter ends with a highlight section, discussing in detail a particularly beautiful or famous result.

Zielgruppe

Professional/practitioner

Autoren/Hrsg.

Aigner, Martin

Fachgebiete

• Mathematik | Informatik Mathematik Algebra
• Mathematik | Informatik Mathematik Operations Research Graphentheorie
• Mathematik | Informatik EDV | Informatik Informatik
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme

Inhaltsverzeichnis

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.