Some Combinatorial Aspects of Reduced Words in Finite Coxeter Groups

We analyze the structure of reduced expressions in the Coxeter groups $A_n$, $B_n$ and $D_n$. Several special classes of elements are singled out for their connections with symmetric functions or the theory of $P$-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.