Coxeter Matroids

Borovik, Alexandre and Gelfand, Israel M. and White, Neil (2003) Coxeter Matroids. Birkhäuser Boston, Boston. ISBN 0817637648

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Abstract

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.

Item Type:	Book
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations
Depositing User:	Ms Lucy van Russelt
Date Deposited:	29 Mar 2007
Last Modified:	08 Jan 2018 11:43
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/746

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