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Coxeter Matroids

  • Alexandre V. Borovik
  • I. M. Gelfand
  • Neil White

Part of the Progress in Mathematics book series (PM, volume 216)

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Alexandre V. Borovik, I. M. Gelfand, Neil White
    Pages 1-36
  3. Alexandre V. Borovik, I. M. Gelfand, Neil White
    Pages 37-53
  4. Alexandre V. Borovik, I. M. Gelfand, Neil White
    Pages 55-80
  5. Alexandre V. Borovik, I. M. Gelfand, Neil White
    Pages 81-99
  6. Alexandre V. Borovik, I. M. Gelfand, Neil White
    Pages 101-149
  7. Alexandre V. Borovik, I. M. Gelfand, Neil White
    Pages 151-197
  8. Alexandre V. Borovik, I. M. Gelfand, Neil White
    Pages 199-252
  9. Back Matter
    Pages 253-266

About this book

Introduction

Matroids appear in diverse areas of mathematics, from combinatorics to algebraic topology and geometry. This largely self-contained text provides an intuitive and interdisciplinary treatment of Coxeter matroids, a new and beautiful generalization of matroids which is based on a finite Coxeter group.

Key topics and features:

* Systematic, clearly written exposition with ample references to current research
* Matroids are examined in terms of symmetric and finite reflection groups
* Finite reflection groups and Coxeter groups are developed from scratch
* The Gelfand-Serganova theorem is presented, allowing for a geometric interpretation of matroids and Coxeter matroids as convex polytopes with certain symmetry properties
* Matroid representations in buildings and combinatorial flag varieties are studied in the final chapter
* Many exercises throughout
* Excellent bibliography and index

Accessible to graduate students and research mathematicians alike, "Coxeter Matroids" can be used as an introductory survey, a graduate course text, or a reference volume.

Keywords

Combinatorics Finite Lattice Permutation Topology algebra geometry mathematics theorem

Authors and affiliations

  • Alexandre V. Borovik
    • 1
  • I. M. Gelfand
    • 2
  • Neil White
    • 3
  1. 1.Department of MathematicsUMISTManchesterUK
  2. 2.Department of MathematicsRutgers UniversityPiscatawayUSA
  3. 3.Department of MathematicsUniversity of FloridaGainesvilleUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-2066-4
  • Copyright Information Birkhäuser Boston 2003
  • Publisher Name Birkhäuser Boston
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-7400-1
  • Online ISBN 978-1-4612-2066-4
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • Buy this book on publisher's site