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Borovik / Gelfand / White

Coxeter Matroids

2003. Buch. xxii, 266 S.: Bibliographien. Hardcover
Birkhäuser ISBN 978-0-8176-3764-4
Format (B x L): 15,5 x 23,5 cm
Gewicht: 620 g
In englischer Sprache
Das Werk ist Teil der Reihe:
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.

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Research

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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 Symplectic matroids and the increasingly general Coxeter matroids are carefully developed The Gelfand-Serganova theorem is presented, allowing for a geometric interpretation of matroids and Coxeter matroids as convex polytopes with certain symmetry properties Matroids representations and combinatorial flag varieties are studied in the final chapter Many exercises throughout Excellent bibliography and index