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.
Rezensionen / Stimmen
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)
