Permanents of doubly stochastic matrices (Q1084155)

Let \(\mu_ k(n)\) denote the minimum value of the permanent of all \(n\times n\) (0,1) matrices whose row and column sums equal k. It has been conjectured that \[ \lim_{n\to \infty}[\mu_ k(n)]^{1/n}=(k-1)^{k- 1}/k^{k-2}. \] The author shows that if \(\prod^{n}_{j=1}\sum^{n}_{i=1}a_{ij}\prod_{k\neq 1}(1- a_{kj})\leq per A\) for any \(n\times n\) doubly stochastic matrix \(A=(a_{ij})\), then the conjecture is valid.