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arXiv · 2105.15195

The upper logarithmic density of monochromatic subset sums

David Conlon·Jacob Fox·Huy Tuan Pham
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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 $(2+\sqrt{3})/4$ and this is best possible. This answers a forty-year-old question of Erdős.

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David Conlon, Jacob Fox, Huy Tuan Pham. 2022-09-22. The upper logarithmic density of monochromatic subset sums. https://arxiv.org/abs/2105.15195

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