Freely braided elements in Coxeter groups, II
Copyright policy )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 (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
- University of Colorado Boulder United States
- Long Island University United States
Generators, relations, and presentations of groups, Free semigroups, generators and relations, word problems, Applied Mathematics, Coxeter group, root systems, root sequences, commutation graphs, Commutation class, Group Theory (math.GR), Graphs and abstract algebra (groups, rings, fields, etc.), Reflection and Coxeter groups (group-theoretic aspects), commutation classes, FOS: Mathematics, simply laced Coxeter groups, Mathematics - Combinatorics, Root sequence, Combinatorics (math.CO), 20F55, Mathematics - Group Theory, Braid relation, braid relations
Generators, relations, and presentations of groups, Free semigroups, generators and relations, word problems, Applied Mathematics, Coxeter group, root systems, root sequences, commutation graphs, Commutation class, Group Theory (math.GR), Graphs and abstract algebra (groups, rings, fields, etc.), Reflection and Coxeter groups (group-theoretic aspects), commutation classes, FOS: Mathematics, simply laced Coxeter groups, Mathematics - Combinatorics, Root sequence, Combinatorics (math.CO), 20F55, Mathematics - Group Theory, Braid relation, braid relations
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