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More than twenty years ago, Manickam, Miklós, and Singhi conjectured that for any integers n, k satisfying n⩾4k, every set of n real numbers with nonnegative sum has at least (n−1k−1) k-element subsets whose sum is also nonnegative. In this paper we discuss the connection of this problem with matchings and fractional covers of hypergraphs, and with the question of estimating the probability that the...
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