Progress in Mathematics

Borovik, Alexandre V.; Borovik, A.; Gelfand, Israel M.; White, Neil

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.

Details

Published by: Birkhäuser

Publication Date: 2003-07-11

Format: Hardcover

ISBN-13: 9780817637644

DOI: 10.1007/978-1-4612-2066-4

Dimensions: 235cm x155cm

Pages: 266