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Let $\mathbb Z/d\mathbb Z \wr \mathfrak S_n$ denote the wreath product of thecyclic group $\mathbb Z/d\mathbb Z$ with the symmetric group $\mathfrak S_n$.We define generating functions for monomial (induced one-dimensional)characters of $\mathbb Z/d\mathbb Z \wr \mathfrak S_n$ and express these interms of determinants and permanents. This extends work of Littlewood ({\em TheTheory of Group Characters and Representations of Groups}, 1940) and Merris andWatkins ({\em Linear Algebra Appl.}, {\bf 64}, 1985) on generating functionsfor the monomial characters of $\mathfrak S_n$.

Generating functions for monomial characters of wreath products $\mathbb Z/d \mathbb Z \wr \mathfrak S_n$