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Counting derangements, involutions and unimodal elements in the wreath product C r ≀ S n

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Abstract

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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Authors and Affiliations

  1. Department of Mathematics and Information Technology, Hong Kong Institute of Education, 10 Lo Ping Road, Tai Po, New Territories, Hong Kong, China

    Chak-On Chow

  2. Department of Mathematics, University of Haifa, 31905, Haifa, Israel

    Toufik Mansour

Authors
  1. Chak-On Chow
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  2. Toufik Mansour
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Correspondence to Chak-On Chow.

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Chow, CO., Mansour, T. Counting derangements, involutions and unimodal elements in the wreath product C r ≀ S n . Isr. J. Math. 179, 425–448 (2010). https://doi.org/10.1007/s11856-010-0088-8

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  • DOI: https://doi.org/10.1007/s11856-010-0088-8

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