 Longest element of a Coxeter group

In the context of Coxeter groups, the **longest element** refers to a particular element of the group that can be identified based on its maximal length with respect to the generating set specified by the Coxeter diagram. A **Coxeter group** is defined by a set of generators and relations that can be represented by a diagram (called a Coxeter diagram) where each generator corresponds to a vertex.