International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 4, Pages 709-716

The Dittert's function on a set of nonnegative matrices

Suk Geun Hwang,1,3 Mun-Gu Sohn,1 and Si-Ju Kim2

1Department of Mathematics, Teachers College, Kyungpook University, Taegu 702-701, Korea
2Department of Mathematics Education, Andong University, Kyungpook, Andong 760-380, Korea
3Department of Mathematics, Sung Kyun Kwan University, Suwon 440-746, Korea

Received 6 November 1989; Revised 12 January 1990

Copyright © 1990 Suk Geun Hwang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let Kn denote the set of all n×n nonnegative matrices with entry sum n. For XKn with row sum vector (r1,,rn), column sum vector (c1,,cn), Let ϕ(X)=iri+jcjperX. Dittert's conjecture asserts that ϕ(X)2n!/nn for all XKn 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.