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The upper logarithmic density of monochromatic subset sums

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.

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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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Conlon, David0000-0001-5899-1829
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]
Funding AgencyGrant Number
David and Lucile Packard FoundationUNSPECIFIED
Two Sigma Investments, LPUNSPECIFIED
Issue or Number:4
Record Number:CaltechAUTHORS:20221017-10817000.4
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:117445
Deposited By: Research Services Depository
Deposited On:20 Oct 2022 17:03
Last Modified:20 Oct 2022 17:03

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