A note on a conjecture on permanents (Q1073874)

The author considers the problem of determining the maximum of the function \[ \psi (X)=\prod^{n}_{i=1}\sum^{n}_{j=1}x_{ij}+\prod^{n}_{j=1}\sum\;sp{n}_{\quad i=1}x_{ij}-per X \] for all nonnegative \(n\times n\) matrices \(X=(x_{ij})\), the sum of whose entries is n. Conditions are given for which the maximum occurs at \(X=J_ n\), the \(n\times n\) matrix whose entries all equal \(n^{-1}\). Some general bounds are given for the row and column sums of a maximizing matrix X.