On the excedance number of colored permutation groups

Eli Bagno, David Garber

Published 2005-05-20Version 1

We generalize the results of Ksavrelof and Zeng about the multidistribution of the excedance number of $S_n$ with some natural parameters to the colored permutation group and to the Coxeter group of type $D$. We define two different orders on these groups which induce two different excedance numbers. Surprisingly, in the case of the colored permutation group, we get the same generalized formulas for both orders.