Freely braided elements in Coxeter groups, II

We continue the study of freely braided elements of simply laced Coxeter groups, which we introduced in a previous work. 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 fr...

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Bibliographic Details
Published in:	Advances in applied mathematics Vol. 33; no. 1; pp. 26 - 39
Main Authors:	Green, R.M., Losonczy, J.
Format:	Journal Article
Language:	English
Published:	San Diego, CA Elsevier Inc 01-07-2004 Elsevier
Subjects:	Braid relation Commutation class Coxeter group Exact sciences and technology Group theory Group theory and generalizations Mathematics Root sequence Sciences and techniques of general use Root sequence Commutation class Braid relation Coxeter group Communication class Applied mathematics Group theory
Online Access:	Get full text
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Summary:	We continue the study of freely braided elements of simply laced Coxeter groups, which we introduced in a previous work. 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.
Bibliography:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	0196-8858 1090-2074
DOI:	10.1016/j.aam.2003.09.003