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It is shown that the polynomial $\lambda(t) = {\rm Tr}[(A + tB)^p]$ hasnonnegative coefficients when $p \leq 7$ and A and B are any two complexpositive semidefinite $n \times n$ matrices with arbitrary $n$. This proofs ageneral nontrivial case of the Lieb-Seiringer formulation of theBessis-Moussa-Villani conjecture which is a long standing problem intheoretical physics.Comment: 5 pages; typos corrected; accepted for publication in Journal of  Statistical Physic

Proof of the Cases p≤ 7 of the Lieb-Seiringer Formulation of the Bessis-Moussa-Villani Conjecture