Permanental pairs of doubly stochastic matrices. II

The n ×n doubly stochastic matrices A, B form a permanental pair if the permanent of every convex linear combination λA+(1?λ)B(0?λ?1) is independent of λ A, B are called mates. In this article we show that the direct sum of any number, k, of matrices J_i (of varying individual dimension) cannot have a mate. Here J_i is the n_i×n_i matrix with every entry equal to $\text{1}\text{n}{}_{\mathrm{i}}$;∑n_i=n.