Statistics on the multi-colored permutation groups (Q870086)

Summary: We define an excedance number for the multi-colored permutation group, i.e. the wreath product \((\mathbb Z_{r_1} \times\cdots\times \mathbb Z_{r_k}) \wr S_n\) 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.