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On the Maximally Clustered Elements of Coxeter Groups
R. M. Green
Department of Mathematics, University of Colorado, Campus Box 395, Boulder, CO 80309-0395, USA
rmg@euclid.colorado.edu
Annals of Combinatorics 14 (4) pp.467-478 December, 2010
AMS Subject Classification: 20F55
Abstract:
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 introduced by 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.
Keywords: contractible triples, highly connected graph

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