Coxeter Matroids (Progress in Mathematics) (Hardcover)

by Alexandre V. Borovik (Author), Israel M. Gelfand (Author), Neil White (Author), A. Borovik (Illustrator)
Key Phrases: Increasing Exchange Property, Symmetric Exchange Axiom, Splitting the Bruhat (more...)

Editorial Reviews

Review

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)

Product Description

Matroids appear in diverse areas of mathematics, from combinatorics to algebraic topology and geometry. This largely self-contained work 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 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.

See all Editorial Reviews

Product Details

• Hardcover: 264 pages
• Publisher: Birkhäuser Boston; 1 edition (July 11, 2003)
• Language: English
• ISBN-10: 0817637648
• ISBN-13: 978-0817637644
• Product Dimensions: 9.3 x 6 x 0.8 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Average Customer Review: No customer reviews yet. Be the first.
• Amazon.com Sales Rank: #2,122,717 in Books (See Bestsellers in Books)
  
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