Combinatorics of Coxeter Groups
Coxeter groups arise in a multitude of ways in several areas of mathem- ics. They are studied in algebra, geometry, and combinatorics, and certain aspects are of importance also in other ?elds of mathematics. The theory of Coxeter groups has been exposited from algebraic and geometric points of view in several places, also in book form. The purpose of this work is to present its core combinatorial aspects. By “combinatoricsof Coxeter groups” we have in mind the mathematics that has to do with reduced expressions, partial order of group elements, enumeration,associatedgraphsand combinatorialcell complexes,andc- nections with combinatorial representation theory. There are some other topics that could also be included under this general heading (e.g., com- natorial properties of re?ection hyperplane arrangements on the geometric side and deeper connections with root systems and representation theory on the algebraic side). However, with the stated aim, there is already more thanplentyofmaterialto?llonevolume,sowiththis “disclaimer”welimit ourselves to the chosen core topics.
Coxeter groups have already been exposited from algebraic and geometric perspectives, but this book will be presenting the combinatorial aspects of Coxeter groups