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Coxeter groups are of central importance in several areas of algebra, geometry, and combinatorics. This clear and rigorous exposition focuses on the combinatorial aspects of Coxeter groups, such as reduced expressions, partial order of group elements, enumeration, associated graphs and combinatorial cell complexes, and connections with combinatorial representation theory. While Coxeter groups have already been exposited from algebraic and geometric perspectives, this text is the first one to focus mainly on the combinatorial aspects of Coxeter groups. The first part of the book provides a self-contained introduction to combinatorial Coxeter group theory. The emphasis here is on the combinatorics of reduced decompositions, Bruhat order, weak order, and some aspects of root systems. The second part deals with more advanced topics, such as Kazhdan-Lusztig polynomials and representations, enumeration, and combinatorial descriptions of the classical finite and affine Weyl groups. A wide variety of exercises, ranging from easy to quite difficult are also included. The book will serve graduate students as well as researchers. Anders Björner is Professor of Mathematics at the Royal Institute of Technology in Stockholm, Sweden. Francesco Brenti is Professor of Mathematics at the University of Rome.

Agrotechnology and Food Sciences. Toxicology --- Toxicity of Pesticides. --- Coxeter groups --- Groupes de Coxeter --- Théorie combinatoire des groupes --- Coxeter groups. --- Kazhdan-Lusztig polynomials. --- Combinatorial groups --- Groups, Combinatorial --- Coxeter's groups --- Real reflection groups --- Reflection groups, Real --- Mathematics. --- Group theory. --- Topological groups. --- Lie groups. --- Combinatorics. --- Topological Groups, Lie Groups. --- Group Theory and Generalizations. --- Combinatorial group theory. --- Combinatorial analysis --- Group theory --- Combinatorial group theory --- Théorie combinatoire des groupes --- EPUB-LIV-FT LIVMATHE SPRINGER-B --- Topological Groups. --- Groups, Topological --- Continuous groups --- Combinatorics --- Algebra --- Mathematical analysis --- Groups, Theory of --- Substitutions (Mathematics) --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Combinatorial analysis.