A Method to Count the Positive 3-Subsets in a Set of Real Numbers with Non-Negative Sum

Abstract

In 1998 Manickam and Singhi [1] stated the following conjecture (conjecture (MS)): if d ∈ N and n ≥ 4d , there exist at least (n−1 d−1 ) d-subsets of {x1, . . . , xr , y1, . . . , yn−r }, i.e., subsets z1, . . . , zd having d elements for which ∑d j=1 z j ≥ 0. This conjecture is in some sense the dual of the theorem of Erdös–Ko–Rado (see [1]). The most… (More)
DOI: 10.1006/eujc.2002.0587

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Cite this paper

@article{Marino2002AMT, title={A Method to Count the Positive 3-Subsets in a Set of Real Numbers with Non-Negative Sum}, author={Giuseppe Marino and Giampiero Chiaselotti}, journal={Eur. J. Comb.}, year={2002}, volume={23}, pages={619-629} }