New results related to a conjecture of Manickam and Singhi

In 1988 Manickam and Singhi conjectured that for every positive integer d and every n ≥ 4 d , every set of n real numbers whose sum is non-negative contains at least ( n − 1 d − 1 ) subsets of size d whose sums are non-negative. In this paper we make use of Hall’s matching theorem in order to study some numbers related to this conjecture.