Lih Wang's and Dittert's conjectures on permanents

Let denote the set of all doubly stochastic matrices of order . Lih and Wang conjectured that for , per per per , for all and all , where is the matrix with each entry equal to . This conjecture was proved partially for . Let denote the set of nonnegative matrices whose elements have sum . Let be a real valued function defined on by - per for with row sum vector and column sum vector . A matrix is called a -maximizing matrix if for all . Dittert conjectured that is the unique -maximizing matrix on . Sinkhorn proved the conjecture for and Hwang proved it for . In this article, we prove the Lih and Wang partially for . It is also proved that if is a -maximizing matrix on , then is fully indecomposable.