Factorizations of signed permutations
Résumé
In this paper we consider a problem related to the factorizations of elements of the wreath product of the symmetric group $\sn$ by $\Z / k\Z$. More precisely, for a given integer $k$, we give a combinatorial construction relating factorizations of elements in the wreath product of $\sn$ by $\Z / k\Z$ and factorizations in $\sn$. Our proof relies on the encoding of such factorizations as maps with signed edges and can be generalized to the factorization of permutations of any cycle type.