On a Problem Concerning the Weight Functions


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… (More)
DOI: 10.1006/eujc.2000.0470