  The randomized $k$-number partitioning problem is the task to distribute $N$
i.i.d. random variables into $k$ groups in such a way that the sums of the
variables in each group are as similar as possible. The restricted
$k$-partitioning problem refers to the case where the number of elements in
each group is fixed to $N/k$. In the case $k=2$ it has been shown that the
properly rescaled differences of the two sums in the close to optimal
partitions converge to a Poisson point process, as if they were independent
random variables. We generalize this result to the case $k>2$ in the restricted
problem and show that the vector of differences between the $k$ sums converges
to a $k-1$-dimensional Poisson point process.
