Generalized Iterated Wreath Products of Symmetric Groups and Generalized Rooted Trees Correspondence

  • Mee Seong Im
  • Angela Wu
Conference paper
Part of the Association for Women in Mathematics Series book series (AWMS, volume 15)


Consider the generalized iterated wreath product \(S_{r_1}\wr \ldots \wr S_{r_k}\) of symmetric groups. We give a complete description of the traversal for the generalized iterated wreath product. We also prove an existence of a bijection between the equivalence classes of ordinary irreducible representations of the generalized iterated wreath product and orbits of labels on certain rooted trees. We find a recursion for the number of these labels and the degrees of irreducible representations of the generalized iterated wreath product. Finally, we give rough upper bound estimates for fast Fourier transforms.


Iterated wreath products Symmetric groups Rooted trees Irreducible representations Fast Fourier transform Bratteli diagrams 

AMS Subject Classification

Primary 20C30 20E08; Secondary 65T50 05E18 05E10 



The authors acknowledge Mathematics Research Communities for providing an exceptional working environment at Snowbird, Utah. They would like to thank Michael Orrison for helpful discussions, and the referees for immensely valuable comments. This paper was written during M.S.I.’s visit to the University of Chicago in 2014. She thanks their hospitality.


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Copyright information

© The Author(s) and the Association for Women in Mathematics 2018

Authors and Affiliations

  • Mee Seong Im
    • 1
  • Angela Wu
    • 2
  1. 1.Department of Mathematical SciencesUnited States Military AcademyWest PointUSA
  2. 2.Department of MathematicsUniversity of ChicagoChicagoUSA

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