Olejar Books

"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."