Chollet's permanent conjecture for $4\times 4$ matrices

Abstract

In the year 1982, John Chollet conjectured that, for any pair of $n\times n$ positive semidefinite matrices $A,B$, $per(A)\cdot per(B)\ge per(A\circ B)$, where $A\circ B$ is the Hardamard product of $A$ and $B$. This conjecture was proved to be valid for $n=2,3$ in the year 1987. In this paper, we show that the conjecture holds true for $n=4$.