Séminaire Combinatoire et Théorie des Nombres ICJ

# The alternating subgroup of the colored permutation group

## par David Garber (Holon Institute of Technology)

Europe/Paris
Bât. Braconnier, salle Fokko du Cloux (ICJ, Université Lyon 1)

### Bât. Braconnier, salle Fokko du Cloux

#### ICJ, Université Lyon 1

Description
The alternating subgroup of the colored permutation group is the natural analogue of the alternating group inside the wreath product (\mathbb{Z}_r \wr S_n\). We present a 'Coxeter like' presentation for this group and calculate the length function with respect to this presentation. Then, we present this group as 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 apply this covering to lift a known parameter of $$\mathbb{Z}_{\frac{r}{2}} \wr S_n$$ to the alternating colored permutation group. Based on a joint work with Eli Bagno and Toufik Mansour.
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