  We describe how previously known methods for determining the number of
decimation classes of density $\delta$ binary vectors can be extended to
nonnegative integer vectors, where the vectors are indexed by a finite abelian
group $G$ of size $\ell$ and exponent $\ell^*$ such that $\delta$ is relatively
prime to $\ell^*$. We extend the previously discovered theory of multipliers
for arbitrary subsets of finite abelian groups, to arbitrary multisets of
finite abelian groups. Moreover, this developed theory provides information on
the number of distinct translates fixed by each member of the multiplier group
as well as sufficient conditions for each member of the multiplier group to be
translate fixing.
