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Statistics on the multi-colored permutation groups. (English) Zbl 1111.05098
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.

##### MSC:
 5e+15 Combinatorial aspects of groups and algebras (MSC2010) 5e+99 Algebraic combinatorics
##### Keywords:
excedance; number of involutions
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