The monotonicity of the permanent function (Q1179284)

The author shows that for each positive integer \(n\) there exists \(\alpha_ n\in(0,1)\) such that \(\text{per}[(1-\theta)J_ n+\theta S]\leq\text{per} S\) for all \(0\leq\theta\leq\alpha_ n\) and all \(n\times n\) doubly stochastic matrices \(S\).