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On the Maximally Clustered Elements of Coxeter Groups

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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 i ji-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 i ji-avoiding elements also turns out to be MC-finite.

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  1. Department of Mathematics, University of Colorado, Campus Box 395, Boulder, CO, 80309-0395, USA

    R. M. Green

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  1. R. M. Green
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Green, R.M. On the Maximally Clustered Elements of Coxeter Groups. Ann. Comb. 14, 467–478 (2010). https://doi.org/10.1007/s00026-011-0071-z

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  • DOI: https://doi.org/10.1007/s00026-011-0071-z

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