Excedances in classical and affine Weyl groups

Based on the notion of colored and absolute excedances introduced by Bagno and Garber we give an analogue of the derangement polynomials. We derive some basic properties of these polynomials. Moreover, we define an excedance statistic for the affine Weyl groups of type B ˜ n , C ˜ n and D ˜ n and determine the generating functions of their distributions. This paper is inspired to one of E. Clark, R. Ehrenborg in which the authors introduce the excedance statistic for the group of affine permutations and ask if this statistic can be defined for other affine groups.