Freely braided elements in Coxeter groups

2003/01/31 by R. M. Green, J. Losonczy · 1 citation
Mathematics · #math.CO #math.GR #msc:20F55

paper · pdf

published as Annals of Combinatorics 6 (2002), 337-348 · 18 pages, AMSTeX. Results renumbered to agree with published version

arxiv created 2003/06/17 · arxiv updated 2009/11/30

Abstract

We introduce a notion of "freely braided element" for simply laced Coxeter groups. We show that an arbitrary group element w has at most 2^N(w) commutation classes of reduced expressions, where N(w) is a certain statistic defined in terms of the positive roots made negative by w. This bound is achieved if w is freely braided. In the type A setting, we show that the bound is achieved only for freely braided w.

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