International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 4, Pages 709-716
doi:10.1155/S0161171290000953
The Dittert's function on a set of nonnegative matrices
Suk Geun Hwang1
, Mun-Go Sohn1
and Si-Ju Kim3
1Department of Mathematics, Teachers College, Kyungpook University, Taegu 702-701, Korea
3Department of Mathematics Education, Andong University, Kyungpook, Andong 760-380, Korea
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.