Geodesic
Computing Reflection Length in an Affine Coxeter Group
Séminaire lotharingien de combinatoire, 80B (2018)

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In any Coxeter group, the conjugates of elements in its Coxeter generating set are called reflections and the reflection length of an element is its length with respect to this expanded generating set. In this article we give a simple formula that computes the reflection length of any element in any affine Coxeter group. In the affine symmetric group, we have a combinatorial formula that generalizes D\'enes' formula for reflection length in the symmetric group. 

@article{SLC_2018_80B_a50,
     author = {Joel Brewster Lewis and Jon McCammond and T. Kyle Petersen and Petra Schwer},
     title = {Computing {Reflection} {Length} in an {Affine} {Coxeter} {Group}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {80B},
     year = {2018},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018_80B_a50/}
}
TY  - JOUR
AU  - Joel Brewster Lewis
AU  - Jon McCammond
AU  - T. Kyle Petersen
AU  - Petra Schwer
TI  - Computing Reflection Length in an Affine Coxeter Group
JO  - Séminaire lotharingien de combinatoire
PY  - 2018
VL  - 80B
PB  - mathdoc
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%0 Journal Article
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%A Jon McCammond
%A T. Kyle Petersen
%A Petra Schwer
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%J Séminaire lotharingien de combinatoire
%D 2018
%V 80B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2018_80B_a50/
%F SLC_2018_80B_a50
Joel Brewster Lewis; Jon McCammond; T. Kyle Petersen; Petra Schwer. Computing Reflection Length in an Affine Coxeter Group. Séminaire lotharingien de combinatoire, 80B (2018). http://geodesic.mathdoc.fr/item/SLC_2018_80B_a50/