| Coxeter Matroids 2003 Edition Contributor(s): Borovik, Alexandre V. (Author), Borovik, A. (Illustrator), Gelfand, Israel M. (Author) |
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ISBN: 0817637648 ISBN-13: 9780817637644 Publisher: Birkhauser OUR PRICE: $104.49 Product Type: Hardcover - Other Formats Published: July 2003 Annotation: Matroids appear in diverse areas of mathematics, from combinatorics to algebraic topology and geometry. This largely self-contained work 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 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. |
| Additional Information |
| BISAC Categories: - Mathematics | Geometry - Algebraic - Medical - Mathematics | Algebra - General |
| Dewey: 511.6 |
| LCCN: 2003045247 |
| Series: Progress in Mathematics |
| Physical Information: 0.74" H x 6.4" W x 9.5" (1.20 lbs) 266 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: Matroids appear in diverse areas of mathematics, from combinatorics to algebraic topology and geometry. This largely self-contained work 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 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. |