Some combinatorial aspects of reduced words in finite Coxeter groups

Source abstract

We analyze the structure of reduced expressions in the Coxeter groups A n A_{n} , B n B_{n} and D n D_{n} . Several special classes of elements are singled out for their connections with symmetric functions or the theory of P P -partitions. Membership in these special classes is characterized in a variety of ways, including forbidden patterns, forbidden subwords, and by the form of canonically chosen reduced words.