Coxeter Matroids (Progress in Mathematics, 216)

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About Coxeter Matroids

Product Description Matroids appear in diverse areas of mathematics, from combinatorics to algebraic topology and geometry, and "Coxeter Matroids" provides an intuitive and interdisciplinary treatment of their theory.  In this text, matroids are examined in terms of symmetric and finite reflection groups; also, symplectic matroids and the more general coxeter matroids are carefully developed. The Gelfand-Serganova theorem, which allows for the geometric interpretation of matroids as convex polytopes with certain symmetry properties, is presented, and in the final chapter, matroid representations and combinatorial flag varieties are discussed. With its excellent bibliography and index and ample references to current research, this work will be useful for graduate students and research mathematicians. Review From the reviews: "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." ― ZENTRALBLATT MATH "...this accessible and well-written book, intended to be "a cross between a postgraduate text and a research monograph," is well worth reading and makes a good case for doing matroids with mirrors." ― SIAM REVIEW "This accessible and well-written book, intended to be ‘a cross between a postgraduate text and a research monograph,’ is well worth reading and makes a good case for doing matroids with mirrors." (Joseph Kung, SIAM Review, Vol. 46 (3), 2004) "This accessible and well-written book, designed to be ‘a cross between a postgraduate text and a research monograph’, should win many converts.”(MATHEMATICAL REVIEWS) From the Back Cover 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.