Permanental mates and Hwangʹs conjecture Original Research Article

Let Ωn denote the set of all n × n doubly stochastic matrices. Two unequal matrices A,B Ωn are said to form a permanental pair if per[tA + (1 − t)B] is constant for all t [0,1], in which case A and B are called permanental mates of each other. We characterize the sets of all matrices in Ω3 and Ω4 having their transpose as permanental mates. Using a generalization of the results, we disprove Hwangʹs conjecture which states that for n ≥ 4, any matrix in the interior of Ωn has no mate.