Coxeter Matroids

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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 indexAccessible to graduate students and research mathematicians alike, Coxeter Matroids can be used as an introductory survey, a graduate course text, or a reference volume.