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

Abstract

Consider the generalized iterated wreath product Sr1≀…≀Srk 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.