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

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Advances in the Mathematical Sciences (AWMRS 2017)

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Abstract

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.

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Acknowledgments

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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Authors and Affiliations

  1. Department of Mathematical Sciences, United States Military Academy, West Point, NY, USA

    Mee Seong Im

  2. Department of Mathematics, University of Chicago, Chicago, IL, USA

    Angela Wu

Authors
  1. Mee Seong Im
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  2. Angela Wu
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Editor information

Editors and Affiliations

  1. Center for Communications Res, San Diego, CA, USA

    Alyson Deines

  2. Department of Mathematics, Texas State University, San Marcos, TX, USA

    Daniela Ferrero

  3. Bryn Mawr College, Ardmore, PA, USA

    Erica Graham

  4. United States Military Academy, New York, NY, USA

    Mee Seong Im

  5. Los Alamos National Laboratory, Los Alamos, NM, USA

    Carrie Manore

  6. Department of Mathematics, University of San Diego, San Diego, CA, USA

    Candice Price

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Im, M.S., Wu, A. (2018). Generalized Iterated Wreath Products of Symmetric Groups and Generalized Rooted Trees Correspondence. In: Deines, A., Ferrero, D., Graham, E., Im, M., Manore, C., Price, C. (eds) Advances in the Mathematical Sciences. AWMRS 2017. Association for Women in Mathematics Series, vol 15. Springer, Cham. https://doi.org/10.1007/978-3-319-98684-5_3

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