  Let $x_1 < \dots < x_n$ and $y_1 < \dots < y_n$, $n \in \mathbb N$, be real
numbers. We show by an example that the assignment problem $$ \max_{\sigma \in
S_n} F_\sigma(x,y) := \frac12 \sum_{i,k=1}^n |x_i - x_k|^\alpha \,
|y_{\sigma(i)} - y_{\sigma(k)}|^\alpha, \quad \alpha >0, $$ is in general
neither solved by the identical permutation (id) nor the anti-identical
permutation (a-id) if $n > 2 +2^\alpha$. Indeed the above maximum can be,
depending on the number of points, arbitrary far away from $F_\text{id}(x,y)$
and $F_\text{a-id}(x,y)$. The motivation to deal with such assignment problems
came from their relation to Gromov-Wasserstein divergences which have recently
attained a lot of attention.
