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On Excess in Finite Coxeter Groups (1405.2701v1)
Published 12 May 2014 in math.GR
Abstract: For a finite Coxeter group $W$ and $w$ an element of $W$ the `excess' of $w$ is defined to be $e(w) = \min{\ell(x) + \ell(y) - \ell(w) \; | \; w=xy, \; x2 = y2 = 1}$ where $\ell$ is the length function on $W$. Here we investigate the behaviour of $e(w)$, 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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