ON THE MONOTONICITY OF THE DITTERT FUNCTION ON CLASSES OF NONNEGATIVE MATRICES

In this paper, we study the monotonicity of the Dittert function (abb. MD) on the line segment from A .mem. $K_{n}$ to J$_{n}$ generalizing both the Dittert conjecture and the Monotonicity conjecture for permanent, and obtain a sufficient condition on A .mem. $K_{n}$ for which the MD holds. It is also proved that if A .mem. $K_{n}$ satisfies the Dokovic inequality (1.2) then MD holds for A, and a subclass of $K_{n}$ for which MD holds is found. is found.