%0 Journal Article
%T Freely braided elements in Coxeter groups
%A R. M. Green
%A J. Losonczy
%J Mathematics
%D 2003
%I arXiv
%X We introduce a notion of "freely braided element" for simply laced Coxeter groups. We show that an arbitrary group element $w$ has at most $2^{N(w)}$ commutation classes of reduced expressions, where $N(w)$ is a certain statistic defined in terms of the positive roots made negative by $w$. This bound is achieved if $w$ is freely braided. In the type $A$ setting, we show that the bound is achieved only for freely braided $w$.
%U http://arxiv.org/abs/math/0301104v2