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The Erdős–Moser Sum-free Set Problem

Part of: Additive number theory; partitions

Published online by Cambridge University Press:  23 September 2019

Tom Sanders
Tom Sanders*
Affiliation:
Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, OxfordOX2 6GG, United Kingdom Email: tom.sanders@maths.ox.ac.uk
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Abstract

We show that there is an absolute $c>0$ such that if $A$ is a finite set of integers, then there is a set $S\subset A$ of size at least $\log ^{1+c}|A|$ such that the restricted sumset $\{s+s^{\prime }:s,s^{\prime }\in S\text{ and }s\neq s^{\prime }\}$ is disjoint from $A$. (The logarithm here is to base $3$.)

Keywords

sum-freesummingFreiman’s theoremadditive energyhereditarily energetic

MSC classification

Primary: 11P70: Inverse problems of additive number theory, including sumsets
Type
Article
Information
Canadian Journal of Mathematics , Volume 73 , Issue 1 , February 2021 , pp. 63 - 107
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Copyright
© Canadian Mathematical Society 2019

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