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

TL;DR

This paper proves Chollet's conjecture for the permanent of 4x4 positive semidefinite matrices, extending the known cases from 2 and 3 to 4.

Contribution

The paper establishes the validity of Chollet's permanent conjecture specifically for 4x4 matrices, filling the gap for this matrix size.

Findings

Chollet's conjecture holds for 4x4 matrices.

The conjecture is verified for all positive semidefinite matrices of size 4.

The result extends the known cases from 2 and 3 to 4.

Abstract

In the year 1982, John Chollet conjectured that, for any pair of $n\times n$ positive semidefinite matrices $A,B$, $per(A)\cdot per(B)\geq per(A\circ B)$, 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 $n=4$.