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2018 | OriginalPaper | Buchkapitel

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

verfasst von : Mee Seong Im, Angela Wu

Erschienen in: Advances in the Mathematical Sciences

Verlag: Springer International Publishing

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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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Vorheriges Kapitel Generalized Iterated Wreath Products of Cyclic Groups and Rooted Trees Correspondence
Nächstes Kapitel Conway–Coxeter Friezes and Mutation: A Survey
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Metadaten
Titel
Generalized Iterated Wreath Products of Symmetric Groups and Generalized Rooted Trees Correspondence
verfasst von
Mee Seong Im
Angela Wu
Copyright-Jahr
2018
Buch
Advances in the Mathematical Sciences

Print ISBN: 978-3-319-98683-8

Electronic ISBN: 978-3-319-98684-5

Copyright-Jahr: 2018

DOI
https://doi.org/10.1007/978-3-319-98684-5_3