Marcus–Newman block permanental inequality conjecture

Let $A$ be partitioned into square blocks as

$$A=\begin{bmatrix}B&C\\ C^*&D\end{bmatrix},$$

where $A$ is positive-semidefinite Hermitian. Marcus–Newman conjecture. For this partition,

$$\mathop{\rm per} A\geqslant (\mathop{\rm per} B)(\mathop{\rm per} D).$$

The conjecture was solved by the corollary cited in the source, so this is a theorem rather than an open conjecture.