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The Dittert's function on a set of nonnegative matrices

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  • Suk Geun Hwang
  • Mun-Gu Sohn
  • Si-Ju Kim

Abstract

Let K n denote the set of all n × n nonnegative matrices with entry sum n . For X ∈ K n with row sum vector ( r 1 , … , r n ) , column sum vector ( c 1 , … , c n ) , Let ϕ ( X ) = ∏ i r i + ∏ j c j − per X . Dittert's conjecture asserts that ϕ ( X ) ≤ 2 − n ! / n n for all X ∈ K n with equality iff X = [ 1 / n ] n × n . This paper investigates some properties of a certain subclass of K n related to the function ϕ and the Dittert's conjecture.

Suggested Citation

  • Suk Geun Hwang & Mun-Gu Sohn & Si-Ju Kim, 1990. "The Dittert's function on a set of nonnegative matrices," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 13, pages 1-8, January.
    • Handle: RePEc:hin:jijmms:794385
    DOI: 10.1155/S0161171290000953
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