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)
Coxeter Matroids
von Alexandre V. Borovik, Israel M. Gelfand und Neil White, illustriert von A. BorovikMatroids 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.
