In this paper, we construct a mixed-base number system over the generalized
symmetric group G(m,1,n), which is a complex reflection group with a root
system of type Bn(m)β. We also establish one-to-one correspondence between
all positive integers in the set {1,β―,mnn!} and the elements of
G(m,1,n) by constructing the subexceedant function in relation to this group.
In addition, we provide a new enumeration system for G(m,1,n) by defining the
inversion statistic on G(m,1,n). Finally, we prove that the
\textit{flag-major index} is equi-distributed with this inversion statistic on
G(m,1,n). Therefore, the flag-major index is Mahonian on G(m,1,n) with
respect to the length function L