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© 2003

Coxeter Matroids

Benefits

  • 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

  • Symplectic matroids and the increasingly general Coxeter matroids are carefully developed

  • The Gelfand-Serganova theorem is presented, allowing for a geometric interpretation of matroids and Coxeter matroids as convex polytopes with certain symmetry properties

  • Matroids representations and combinatorial flag varieties are studied in the final chapter

  • Many exercises throughout

  • Excellent bibliography and index

Textbook

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

  1. 1.Department of MathematicsUMISTManchesterUK
  2. 2.Department of MathematicsRutgers UniversityPiscatawayUSA
  3. 3.Department of MathematicsUniversity of FloridaGainesvilleUSA

Bibliographic information

  • Book Title Coxeter Matroids
  • Authors Alexandre V. Borovik
    Israel M. Gelfand
    Neil White
  • Series Title Progress in Mathematics
  • Series Abbreviated Title Progress in Mathematics(Birkhäuser)
  • 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
  • Hardcover ISBN 978-0-8176-3764-4
  • Softcover ISBN 978-1-4612-7400-1
  • eBook ISBN 978-1-4612-2066-4
  • Series ISSN 0743-1643
  • Series E-ISSN 2296-505X
  • Edition Number 1
  • Number of Pages XXII, 266
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Algebraic Geometry
    Mathematics, general
    Algebra
    Combinatorics
  • Buy this book on publisher's site
Industry Sectors
Finance, Business & Banking

Reviews

From the reviews:

"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."

— ZENTRALBLATT MATH

"...this accessible and well-written book, intended to be "a cross between a postgraduate text and a research monograph," is well worth reading and makes a good case for doing matroids with mirrors."

— SIAM REVIEW

"This accessible and well-written book, intended to be ‘a cross between a postgraduate text and a research monograph,’ is well worth reading and makes a good case for doing matroids with mirrors." (Joseph Kung, SIAM Review, Vol. 46 (3), 2004)

"This accessible and well-written book, designed to be ‘a cross between a postgraduate text and a research monograph’, should win many converts.”(MATHEMATICAL REVIEWS)