Let and be two integers such that ; we denote by the minimum [maximum] number of the nonnegative partial sums of a sum , where are real numbers arbitrarily chosen in such a way that of them are nonnegative and the remaining are negative. We study the following two problems: which are the values of and for each and , ? if is an integer such that , can we find real numbers , such that of them are nonnegative and the remaining are negative with , such that the number of the nonnegative sums formed from these numbers is exactly ?
"A Minimum Problem for Finite Sets of Real Numbers with Nonnegative Sum." J. Appl. Math. 2012 (SI03) 1 - 15, 2012. https://doi.org/10.1155/2012/847958