Coxeter Matroids
By: by Alexandre V. Borovik, I. M. Gelfand, Neil White
Contributors: Gelfand, I. M.; White, Neil
Series: Progress in Mathematics -- 216; Progress in Mathematics -- 216
Publisher: Birkhäuser Boston
Published: 2003
Place of publication: Boston, MA
Language: eng
Format: [electronic resource] /
Number of pages: 264
ISBN-13: 9781461274001; 9781461220664
Subjects: Mathematics; Algebraic Geometry; Combinatorial analysis; Algebra
Description: 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.
Notes: Online full text is restricted to subscribers.

Also available in print.

Mode of access: World Wide Web.
Table of contents: title: Introduction; title: Foreword for the Expert Reader; title: Matroids and Flag Matroids; title: Matroids and Semimodular Lattices; title: Symplectic Matroids; title: Lagrangian Matroids; title: Reflection Groups and Coxeter Groups; title: Coxeter Matroids; title: Buildings; title: Bibliography; title: Index.