Séminaire Lotharingien de Combinatoire, 78B.45 (2017), 12 pp.
On Cycle Decompositions in Coxeter Groups
The aim of this note is to show that the cycle decomposition of
elements of the symmetric group admits a quite natural formulation in
the framework of dual Coxeter theory, allowing a generalization of it
to the family of so-called parabolic quasi-Coxeter elements
of Coxeter groups (in the symmetric group every element is a parabolic
quasi-Coxeter element). We show that such an element admits an
analogue of the cycle decomposition. Elements which are not in this
family still admit a generalized cycle decomposition, but it is not
unique in general.
Received: November 14, 2016.
Accepted: February 17, 2017.
Final version: April 1, 2017.
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