  We consider, after Albouy-Moeckel, the inverse problem for collinear central
configurations: given a collinear configuration of $n$ bodies, find positive
masses which make it central. We give some new estimates concerning the
positivity of Albouy-Moeckel pfaffians: we show that for any homogeneity
$\alpha$ and $n\leq 6$ or $n\leq 10$ and $\alpha=1$ (computer-assisted) the
pfaffians are positive. Moreover, for the inverse problem with positive masses,
we show that for any homogeneity and $n\geq 4$ there are explicit regions of
the configuration space without solutions of the inverse problem.
