The upper logarithmic density of monochromatic subset sums

Abstract

We show that in any two-coloring of the positive integers there is a color for which the set of positive integers that can be represented as a sum of distinct elements with this color has upper logarithmic density at least ( 2 + 3 ) / 4 $(2+\sqrt {3})/4$ and this is best possible. This answers a 40-year-old question of Erdős.

Locations

• arXiv (Cornell University) - View - PDF
• Mathematika - View