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

Pfaffians and the inverse problem for collinear central configurations