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Let Kn denote the set of all nÃƒÂ—n nonnegative matrices with entry sum n. For XÃ¢ÂˆÂˆKn with row sum vector (r1,Ã¢Â€Â¦,rn), column sum vector (c1,Ã¢Â€Â¦,cn), Let ÃÂ•(X)=Ã¢ÂˆÂiri+Ã¢ÂˆÂjcjÃ¢ÂˆÂ’perX. Dittert's conjecture asserts that ÃÂ•(X)Ã¢Â‰Â¤2Ã¢ÂˆÂ’n!/nn for all XÃ¢ÂˆÂˆKn with equality iff X=[1/n]nÃƒÂ—n. This paper investigates some properties of a certain subclass of Kn related to the function ÃÂ• and the Dittert's conjecture

The Dittert's function on a set of nonnegative matrices