On excess in finite Coxeter groups

Hart, Sarah and Rowley, P.J. (2015) On excess in finite Coxeter groups. Journal of Pure and Applied Algebra 219 (5), pp. 1657-1669. ISSN 0022-4049.

Abstract

For a finite Coxeter group W and w an element of W the excess of w is defined to be View the MathML sourcee(w)=min{ℓ(x)+ℓ(y)−ℓ(w)|w=xy,x2=y2=1} where ℓ is the length function on W . Here we investigate the behaviour of e(w)e(w), and a related concept reflection excess, when restricted to standard parabolic subgroups of W. Also the set of involutions inverting w is studied.

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