Statistics on the multi-colored permutation groups
Abstract
We define an excedance number for the multi-colored permutation group, i.e. the wreath product of Zr1 x ... x Zrk with Sn, 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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