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On a Problem Concerning the Weight Functions

✍ Scribed by Giampiero Chiaselotti

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 75 KB
Volume: 23
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.2000.0470

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✦ Synopsis

GIAMPIERO CHIASELOTTI †

Let X be a finite set with n elements. A function f : X -→ R such that x∈X f (x) ≥ 0 is called a n-weight function. In 1988 Manickam and Singhi conjectured that, if d is a positive integer and f is a n-weight function with n ≥ 4d there exist at least n-1 d-1 subsets Y of X with |Y | = d for which y∈Y f (y) ≥ 0. In this paper we study this conjecture and we show that it is true if f is a n-weight function and |{x ∈ X : f (x) ≥ 0}| ≤ d ≤ n 2 .

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