On the group of alternating colored permutations

Abstract

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.

29 pages, one figure; submitted

References in corpus (2)

• Statistics on Wreath Products
• On the excedance number of colored permutation groups