On Excess in Finite Coxeter Groups

2014/05/12 by Hart, Sarah B., Rowley, Peter J.
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1405.2701

Abstract

For a finite Coxeter group W and w an element of W the `excess' of w is defined to be e(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), 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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