On the maximally clustered elements of Coxeter groups

Details On the maximally clustered elements of Coxeter groups On the maximally clustered elements of Coxeter groups

2007-03-14

arxiv.org/abs/math/0703435v1

Mathematics

Combinatorics

Approximately 18 pages, AMSTeX. One non-essential figure

Scientific paper

We continue the study of the maximally clustered elements for simply laced Coxeter groups which were recently introduced by Losonczy. Such elements include as a special case the freely braided elements of Losonczy and the author, which in turn constitute a superset of the $iji$-avoiding elements of Fan. Our main result is to classify the MC-finite Coxeter groups, namely those Coxeter groups having finitely many maximally clustered elements. Remarkably, any simply laced Coxeter group having finitely many $iji$-avoiding elements also turns out to be MC-finite.

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