Statistics on the Multi-Colored Permutation Groups

Eli Bagno, Ayelet Butman, David Garber

Abstract


We define an excedance number for the multi-colored permutation group i.e. the wreath product $({\Bbb Z}_{r_1} \times \cdots \times {\Bbb Z}_{r_k}) \wr S_n$ 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.


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