Titlebook: Coxeter Matroids; Alexandre V. Borovik,I. M. Gelfand,Neil White Textbook 20031st edition Birkhäuser Boston 2003 Combinatorics.Finite.Latti

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0743-1643 ection groups.Finite reflection groups and Coxeter groups ar.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 general

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metric that gives it a structure only slightly weaker than that of a building over .. This leads to a natural way to represent flag matroids in semimodular lattices, which in turn leads up to our representation of arbitrary Coxeter matroids in buildings in Chapter 7.

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Reflection Groups and Coxeter Groups,. of W) form the language of the theory of Coxeter matroids. The reader familiar with the theory of reflection groups and Coxeter groups may skip most of the chapter. However, we recommend that this reader look through Sections 5.12 “Residues,” 5.14 “Bruhat order” and 5.15 “Splitting the Bruhat order.”

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