Permanental Mates: Perturbations and Hwang’s conjecture

Let ΩnΩn denote the set of all n×nn×n doubly stochastic matrices. Two unequal matrices AA and BB in ΩnΩn are called permanental mates if the permanent function is constant on the line segment tA+(1−t)B,0≤t≤1, connecting AA and BB. We study the perturbation matrix A+EA+E of a symmetric matrix AA in ΩnΩn as a permanental mate of AA. Also we show an example to disprove Hwang’s conjecture, which states that, for n≥4n≥4, any matrix in the interior of ΩnΩn has no permanental mate.