We count derangements, involutions and unimodal elements in the wreath product C r ≀ S n by the numbers of excedances, fixed points and 2-cycles. Properties of the generating functions, including combinatorial formulas, recurrence relations and real-rootedness are studied. The results obtained specialize to those on the symmetric group S n and on the hyperoctahedral group B n when r = 1, 2, respectively.
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机译：我们用兴奋度，不动点数和2个周期的数量计算花圈乘积C r ≀S n 中的混乱，对合和单峰元素。研究了生成函数的性质，包括组合公式，递归关系和实根。当r = 1、2时，分别获得对称对称群S n 和超八面体群B n 的结果。
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