The group of alternating colored permutations is the natural analogue of the classical alternating group, inside the wreath product $\mathbb{Z}_r \wr S_n$. We present a 'Coxeter-like' presentation for this group and compute the length function with respect to that presentation. Then, we present this group as a covering of $\mathbb{Z}_{\frac{r}{2}} \wr S_n$ and use this point of view to give another expression for the length function. We also use this covering to lift several known parameters of $\mathbb{Z}_{\frac{r}{2}} \wr S_n$ to the group of alternating colored permutations.
@article{10_37236_3974,
author = {Eli Bagno and David Garber and Toufik Mansour},
title = {On the group of alternating colored permutations.},
journal = {The electronic journal of combinatorics},
year = {2014},
volume = {21},
number = {2},
doi = {10.37236/3974},
zbl = {1298.20002},
url = {http://geodesic.mathdoc.fr/articles/10.37236/3974/}
}
TY - JOUR
AU - Eli Bagno
AU - David Garber
AU - Toufik Mansour
TI - On the group of alternating colored permutations.
JO - The electronic journal of combinatorics
PY - 2014
VL - 21
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/3974/
DO - 10.37236/3974
ID - 10_37236_3974
ER -
%0 Journal Article
%A Eli Bagno
%A David Garber
%A Toufik Mansour
%T On the group of alternating colored permutations.
%J The electronic journal of combinatorics
%D 2014
%V 21
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/3974/
%R 10.37236/3974
%F 10_37236_3974
Eli Bagno; David Garber; Toufik Mansour. On the group of alternating colored permutations.. The electronic journal of combinatorics, Tome 21 (2014) no. 2. doi: 10.37236/3974
