Geodesic
On Cycle Decompositions in Coxeter Groups
Séminaire lotharingien de combinatoire, 78B (2017)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

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},
     publisher = {mathdoc},
     volume = {78B},
     year = {2017},
     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
PB  - mathdoc
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
%I mathdoc
%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/