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Coxeter Matroids. Softcover reprint of the original 1st ed. 2003.
・ISBN 978-1-4612-7400-1 paper EUR 49.99
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| 著者・編者 | Borovik, Alexandre V. / Gelfand, Israel M. / White, Neil, |
|---|---|
| シリーズ | Progress in Mathematics |
| 出版社 | (Springer-Verlag New York Inc., US) |
| 出版年月 | 2011 |
| ページ数 | 266 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-23586＞ |
解説
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.