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The reformulation of the Bessis-Moussa-Villani conjecture given by Lieb andSeiringer asserts that the coefficient of t^r in the polynomialTrace[(A+tB)^p], with A and B positive semidefinite matrices, is nonnegativefor all p and r. We propose a natural extension of a method of attack on thisproblem due to Haegele, and investigate for what values of p and r the methodis successful, obtaining a complete determination when either p or r is odd.

On D. Haegele's approach to the Bessis-Moussa-Villani conjecture