On Excess in Finite Coxeter Groups

Sarah B. Hart, Peter J. Rowley

For a finite Coxeter group $W$ and $w$ an element of $W$ the `excess' of $w$ is defined to be $e(w)=\min \{\ell (x)+\ell (y)-\ell (w)|w=xy,x^2=y^2=1\}$ where $\el…