2003/10/08 by R. M. Green, Jozsef Losonczy, Green, R. M. +2
Computer Science · Materials Science · Mathematics · #Algebraic structures and combinatorial models #Supramolecular Self-Assembly in Materials #math.CO #math.GR #msc:20F55 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.math/0310120
AMSTeX, approximately 19 pages
arxiv created 2003/10/08 · arxiv updated 2009/12/01
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.