Overview
- 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
Part of the book series: Progress in Mathematics (PM, volume 216)
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Table of contents (7 chapters)
Keywords
About this book
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.
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)
Authors and Affiliations
Bibliographic Information
Book Title: Coxeter Matroids
Authors: Alexandre V. Borovik, I. M. Gelfand, Neil White
Series Title: Progress in Mathematics
DOI: https://doi.org/10.1007/978-1-4612-2066-4
Publisher: Birkhäuser Boston, MA
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eBook Packages: Springer Book Archive
Copyright Information: Birkhäuser Boston 2003
Hardcover ISBN: 978-0-8176-3764-4Published: 11 July 2003
Softcover ISBN: 978-1-4612-7400-1Published: 16 September 2011
eBook ISBN: 978-1-4612-2066-4Published: 06 December 2012
Series ISSN: 0743-1643
Series E-ISSN: 2296-505X
Edition Number: 1
Number of Pages: XXII, 266
Topics: Algebraic Geometry, Mathematics, general, Algebra, Combinatorics