Bapat–Sunder's permanent Hadamard-product inequality

Let $\mathcal{H}_n$ be the set of $n\times n$ positive semidefinite Hermitian matrices. For matrices $A=[a_{i,j}]$ and $B=[b_{i,j}]$ in $\mathcal{H}_n$, define the Hadamard product by $(A\circ B)=[a_{i,j}b_{i,j}]$. Bapat–Sunder's conjecture. If $A,B\in\mathcal{H}_n$, then

$$\operatorname{per}(A\circ B)\leq \operatorname{per}(A)\prod_{i=1}^n b_{i,i}.$$

This is the permanental counterpart of Oppenheim's determinant inequality. The conjecture was disproved by Drury; the status is therefore refuted.