Nonnegative k-sums, fractional covers, and probability of small deviations

Noga Alon, Hao Huang, Benny Sudakov

More than twenty years ago, Manickam, Miklós, and Singhi conjectured that for any integers $n,k$ satisfying $n\ge 4k$, every set of $n$ real numbers with nonnegative sum has at…