Combinatorics of Coxeter Groups

  • Anders Bjorner
  • Francesco Brenti
Part of the Graduate Texts in Mathematics book series (GTM, volume 231)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Part I

    1. Pages 1-25
    2. Pages 27-64
  3. Part II

  4. Back Matter
    Pages 295-363

About this book

Introduction

Coxeter groups are of central importance in several areas of algebra, geometry, and combinatorics. This  clear and rigorous exposition focuses on the combinatorial aspects of Coxeter groups, such as reduced expressions, partial order of group elements, enumeration, associated graphs and combinatorial cell complexes, and connections with combinatorial representation theory.  While Coxeter groups have already been exposited from algebraic and geometric perspectives, this text is the first one to focus mainly on the combinatorial aspects of Coxeter groups.

The first part of the book provides a self-contained introduction to combinatorial Coxeter group theory. The emphasis here is on the combinatorics of reduced decompositions, Bruhat order, weak order, and some aspects of root systems.  The second part deals with more advanced topics, such as Kazhdan-Lusztig polynomials and representations, enumeration, and combinatorial descriptions of the classical finite and affine Weyl 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.

Anders Björner is Professor of Mathematics at the Royal Institute of Technology in Stockholm, Sweden. Francesco Brenti is Professor of Mathematics at the University of Rome.

Keywords

Combinatorics algebra graphs representation theory

Authors and affiliations

  • Anders Bjorner
    • 1
  • Francesco Brenti
    • 2
  1. 1.Department of MathematicsRoyal Institute of TechnologyStockholmSweden
  2. 2.Dipartimento di MatematicaUniversita di RomaRomaItaly

Bibliographic information

  • DOI https://doi.org/10.1007/3-540-27596-7
  • Copyright Information Springer Science+Business Media, Inc. 2005
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-44238-7
  • Online ISBN 978-3-540-27596-1
  • Series Print ISSN 0072-5285
  • About this book