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The monotonicity of the permanent function. (English) Zbl 0748.15007
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 \(S\).
15A15 Determinants, permanents, traces, other special matrix functions
15B51 Stochastic matrices
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