Conlon, David and Fox, Jacob and Pham, Huy Tuan (2022) The upper logarithmic density of monochromatic subset sums. Mathematika, 68 (4). pp. 1292-1301. ISSN 0025-5793. doi:10.1112/mtk.12167. https://resolver.caltech.edu/CaltechAUTHORS:20221017-10817000.4
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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 + √3)/4 and this is best possible. This answers a 40-year-old question of Erdős.
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| 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] | ||||||||||||
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| Issue or Number: | 4 | ||||||||||||
| DOI: | 10.1112/mtk.12167 | ||||||||||||
| Record Number: | CaltechAUTHORS:20221017-10817000.4 | ||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20221017-10817000.4 | ||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
| ID Code: | 117445 | ||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||
| Deposited By: | Research Services Depository | ||||||||||||
| Deposited On: | 20 Oct 2022 17:03 | ||||||||||||
| Last Modified: | 20 Oct 2022 17:03 |
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