Statistics on the Multi-Colored Permutation Groups

We define an excedance number for the multi-colored permutation group i.e. the wreath product (Zr-1 x...x Zr-k) S-n and calculate its multi-distribution with some natural parameters. We also compute the multi-distribution of the parameters exc(pi) and fix(pi) over the sets of involutions in the multi-colored permutation group. Using this, we count the number of involutions in this group having a fixed number of excedances and absolute fixed points.