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Freely braided elements in Coxeter groups, II

R. M. Green·J. Losonczy
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Abstract

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.

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R. M. Green, J. Losonczy. 2003-10-08. Freely braided elements in Coxeter groups, II. https://arxiv.org/abs/math/0310120

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