The upper logarithmic density of monochromatic subset sums
Combinatorics
2022-09-23 v3 Number Theory
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 and this is best possible. This answers a forty-year-old question of Erd\H{o}s.
Cite
@article{arxiv.2105.15195,
title = {The upper logarithmic density of monochromatic subset sums},
author = {David Conlon and Jacob Fox and Huy Tuan Pham},
journal= {arXiv preprint arXiv:2105.15195},
year = {2022}
}
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9 pages