Bruhat ordering

• Let $W$ be a Coxeter group

def (Bruhat ordering)

Define a partial order on the elements of $W$ as follows :

The vertex set is the set of elements of the Coxeter group and the edge set consists of directed edges $(u, v)$ whenever $u = t v$ for some reflection $t$ and $\ell(u) < \ell(v)$.

• example : http://groupprops.subwiki.org/wiki/File:Bruhatons3.png