Lieb–Seiringer reformulation of the Bessis–Moussa–Villani conjecture

Let $A$ and $B$ be $n \times n$ positive semidefinite matrices, and let $m$ and $r$ be integers with $m \geq r \geq 0$. Lieb–Seiringer's conjecture. The coefficient of $t^r$ in

$$\operatorname{trace}((A+tB)^m)$$

is non-negative. This is a reformulation of the Bessis–Moussa–Villani conjecture, which was proved by Stahl in 2013; the stated positivity claim is therefore solved.