  An indecomposable decomposition of a torsion-free abelian group $G$ of rank
$n$ is a decomposition $G=A_1\oplus\cdots\oplus A_t$ where $A_i$ is
indecomposable of rank $r_i$ so that $\sum_i r_i=n$ is a partition of $n$. The
group $G$ may have decompositions that result in different partitions of $n$.
We address the problem of characterising those sets of partitions of $n$ which
can arise from indecomposable decompositions of a torsion-free abelian group.
