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Published October 2022 | public
Journal Article

The upper logarithmic density of monochromatic subset sums


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 and this is best possible. This answers a 40-year-old question of Erdős.

Additional Information

Research supported by NSF Award DMS-2054452. [Conlon] Research supported by a Packard Fellowship and by NSF Awards DMS-1855635 and DMS-2154169. [Fox] Research supported by a Two Sigma Fellowship. [Pham]

Additional details

August 22, 2023
October 24, 2023