2007.48: Coxeter Matroids

2007.48: A. Borovik, Israel M. Gelfand and Neil White (2003) Coxeter Matroids. Birkhäuser Boston, Boston. ISBN 0817637648

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Official URL: http://www.amazon.com/Coxeter-Matroids-Progress-Mathematics-Alexandre/dp/0817637648

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.

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