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

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.

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