Freely braided elements in Coxeter groups, II

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We continue the study of freely braided elements of simply laced Coxeter groups, which we introduced in a previous work (math.CO/0301104). A known upper bound for the number of commutation classes of reduced expressions for an element of a simply laced Coxeter group is shown to be achieved only when the element is freely braided; this establishes the converse direction of a previous result. It is also shown that a simply laced Coxeter group has finitely many freely braided elements if and only if it has finitely many fully commutative elements.
AMSTeX, approximately 19 pages

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Combinatorics, Group Theory, 20F55

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http://salesiana.dossiersoluciones.com/handle/123456789/68786

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0310120
 http://arxiv.org/abs/math/0310120

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arXiv