2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66228We 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 $w$.18 pages, AMSTeX. Results renumbered to agree with published versionCombinatoricsGroup Theory20F55text