Some new results on subset sums (Q877934)

Let \(f(n)\) denote the smallest integer \(f\) such that one can color the integers \(\{1, 2, \dots,n-1\}\) by \(f\) colors so that there is no monochromatic subset the sum of whose elements is \(n\). The author improves the lower bound of a two-sided estimation given by \textit{N. Alon} and \textit{P. Erdős} [Acta Arith. 74, No.~3, 269--272 (1996; Zbl 0838.11018)] showing that \(c_1 n^{1/3}/\log n \leq f(n)\) for a positive constant \(c_1\). Some new related results are also discussed in the paper.