The Dittert's function on a set of nonnegative matrices

Abstract

Let Kn denote the set of all n×n nonnegative matrices with entry sum n. For X∈Kn with row sum vector (r1,…,rn), column sum vector (c1,…,cn), Let ϕ(X)=∏iri+∏jcj−perX. Dittert's conjecture asserts that ϕ(X)≤2−n!/nn for all X∈Kn with equality iff X=[1/n]n×n. This paper investigates some properties of a certain subclass of Kn related to the function ϕ and the Dittert's conjecture.