Combinatorics of Coxeter Groups

by Anders Bjorner, Francesco Brenti

Overview

This book is a carefully written exposition of Coxeter groups, an area of mathematics which appears in algebra, geometry, and combinatorics. In this book, the combinatorics of Coxeter groups has mainly to do with reduced expressions, partial order of group elements, enumeration, associated graphs and combinatorial cell complexes, and connections with combinatorial representation theory. The authors have included exposition along with a rich selection of exercises.

Product Details

ISBN-13:	9783540442387
Publisher:	Springer Berlin Heidelberg
Publication date:	05/31/2005
Series:	Graduate Texts in Mathematics , #231
Edition description:	2005
Pages:	366
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

I.- The basics.- Bruhat order.- Weak order and reduced words.- Roots, games, and automata.- II.- Kazhdan-Lusztig and R-polynomials.- Kazhdan-Lusztig representations.- Enumeration.- Combinatorial Descriptions.

Editorial Reviews

From the reviews:

"Coxeter groups are groups which are generated by involutions. … are written in a very expository manner, and serve as a very nice introduction to the subject which a graduate student would be able to follow. … chapters are self-contained, and the book has several appendices to help the reader who does not have the full background." (Darren Glass, MathDL, May, 2005)

"The book under review presents the combinatorial aspects in the theory of Coxeter groups. … Plenty of exercises are provided in each chapter, ranging from easier ones to more difficult ones and open problems. … More than 500 references related to the above topics are attached at the end of the book. Thus the book is suitable both as a graduate textbook (particularly Part I) and as a research monograph (particularly Part II) for the combinatorics of Coxeter groups." (Jian-yi Shi, Mathematical Reviews, Issue 2006 d)

"This is the first one to focus mainly on the combinatorial aspects of Coxeter groups. … A wide variety of exercises, ranging from easy to quite difficult are also included. The book will serve graduate students as well as researchers." (L'Enseignement Mathématique, Vol. 51 (3-4), 2005)

"The general theory of Coxeter groups naturally involves combinatorics, geometry and algebra. The aim of the book under review is to present the core combinatorial aspects of the theory of Coxeter groups. … Endnotes to each chapter provide historical connections and for related materials, including the algebraic and geometric aspects of the topics. Four appendices and a comprehensive bibliography containing 559 entries complete this book to a useful research monograph. … the book is also well suited to serve as a graduate textbook." (Herman J. Servatius, Zentralblatt MATH, Vol. 1110 (12), 2007)

From the Publisher