A Minimum Problem for Finite Sets of Real Numbers with Nonnegative Sum


Let n and r be two integers such that 0 < r ≤ n; we denote by γ(n, r) [η(n, r)] the minimum [maximum] number of the non-negative partial sums of a sum ∑ n 1=1 ai ≥ 0, where a1, · · · , an are n real numbers arbitrarily chosen in such a way that r of them are non-negative and the remaining n − r are negative. Inspired by some interesting extremal… (More)
DOI: 10.1155/2012/847958