Sharp Bound for the Erdős–Straus Non-averaging Set Problem
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39_2025_Article_728.pdf
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1.47 MB
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51b1573e10c3094b3b15f9c0bf959e7f
Author(s)
Pham, Huy T.
Zakharov, Dmitrii
Date Issued
December 3, 2025
Journal
Geometric and Functional Analysis
Publisher
Springer International Publishing
Citation
Pham, H.T., Zakharov, D. Sharp Bound for the Erdős–Straus Non-averaging Set Problem. Geom. Funct. Anal. (2025).
Version
Final published version
Abstract
A set of integers A is non-averaging if there is no element a in A which can be written as an average of a subset of A not containing a . We show that the largest non-averaging subset of { 1 , … , n } has size n 1 / 4 + o ( 1 ) , thus solving the Erdős–Straus problem. We also determine the largest size of a non-averaging set in a d -dimensional box for any fixed d . Our main tool includes the structure theorem for the set of subset sums due to Conlon, Fox and the first author, together with a result about the structure of a point set in nearly convex position.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s00039-025-00728-8
