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arXiv · 1405.2701

On Excess in Finite Coxeter Groups

Sarah B. Hart·Peter J. Rowley
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Abstract

For a finite Coxeter group $W$ and $w$ an element of $W$ the `excess' of $w$ is defined to be $e(w) = \min\{\ell(x) + \ell(y) - \ell(w) \; | \; w=xy, \; x^2 = y^2 = 1\}$ 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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Sarah B. Hart, Peter J. Rowley. 2014-05-12. On Excess in Finite Coxeter Groups. https://arxiv.org/abs/1405.2701

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