On Excess in Finite Coxeter Groups

Sarah B. Hart; Peter J. Rowley

On Excess in Finite Coxeter Groups

Group Theory 2014-05-13 v1

Authors: Sarah B. Hart , Peter J. Rowley

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.

Keywords

coxeter groups combinatorial group theory

Cite

@article{arxiv.1405.2701,
  title  = {On Excess in Finite Coxeter Groups},
  author = {Sarah B. Hart and Peter J. Rowley},
  journal= {arXiv preprint arXiv:1405.2701},
  year   = {2014}
}

Comments

This is a preprint version. It has been accepted, subject to revision, in J. Pure Appl. Alg

On Excess in Finite Coxeter Groups

Abstract

Keywords

Cite

Comments

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