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Freely Braided Elements in Coxeter Groups
R.M. Green1 and J. Losonczy2
1Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, England
2Department of Mathematics, Long Island University, Brookville, NY 11548, USA
Annals of Combinatorics 6 (3) p.337-348 September, 2002
AMS Subject Classification: 20F55
We introduce a notion of ``freely braided element" for simply laced Coxeter groups. We show that an arbitrary group element w has at most 2N(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.
Keywords: braid relation, commutation class, Coxeter group, root sequence


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