In mathematics, the longest element of a Coxeter group is the unique element of maximal length in a finite Coxeter group with respect to the chosen generating set consisting of simple reflections.
It is often denoted by w0.
See (Humphreys 1992, Section 1.8: Simple transitivity and the longest element, pp.
15–16) and (Davis 2007, Section 4.6, pp.
51–53).