Geodesic
On Cycle Decompositions in Coxeter Groups
Séminaire lotharingien de combinatoire, 78B (2017) Cet article a éte moissonné depuis la source Séminaire Lotharingien de Combinatoire website

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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. 

@article{SLC_2017_78B_a44,
     author = {Thomas Gobet},
     title = {On {Cycle} {Decompositions} in {Coxeter} {Groups}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2017},
     volume = {78B},
     url = {http://geodesic.mathdoc.fr/item/SLC_2017_78B_a44/}
}
TY  - JOUR
AU  - Thomas Gobet
TI  - On Cycle Decompositions in Coxeter Groups
JO  - Séminaire lotharingien de combinatoire
PY  - 2017
VL  - 78B
UR  - http://geodesic.mathdoc.fr/item/SLC_2017_78B_a44/
ID  - SLC_2017_78B_a44
ER  - 
%0 Journal Article
%A Thomas Gobet
%T On Cycle Decompositions in Coxeter Groups
%J Séminaire lotharingien de combinatoire
%D 2017
%V 78B
%U http://geodesic.mathdoc.fr/item/SLC_2017_78B_a44/
%F SLC_2017_78B_a44
Thomas Gobet. On Cycle Decompositions in Coxeter Groups. Séminaire lotharingien de combinatoire, 78B (2017). http://geodesic.mathdoc.fr/item/SLC_2017_78B_a44/