Miklos Dezső:
On the number of postive subsums of a positive sum
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Let n_0(k) denote the minimum value of n such that for every a_1,
....  ,   a_n real numbers with positive sum the minimum
number of the k-subsets of the set {a_1,    ....  ,   a_n}  with
positive sum too is {n-1 \choose k-1}. The Manickam-Miklos-Singhi
conjecture says that n_0(k) \le 4k.  Recent results toward this
conjecture from different authors will be presented.