Bapat–Sunder's largest-eigenvalue conjecture for the permanent matrix

Let $\mathcal{H}_n$ be the set of $n\times n$ positive semidefinite Hermitian matrices. For $A=[a_{i,j}]\in\mathcal{H}_n$, let $A(i,j)$ be the submatrix obtained by deleting row $i$ and column $j$, and define $F_A=[f_{i,j}]$ by

$$f_{i,j}=a_{i,j}\operatorname{per}(A(i,j)).$$

Bapat–Sunder's conjecture. The largest eigenvalue of $F_A$ should satisfy

$$\lambda_{\max}(F_A)\leq \operatorname{per}(A).$$

Equivalently, $\operatorname{per}(A)$ should be the largest eigenvalue of $F_A$. Drury disproved this conjecture, so it is refuted.