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THE CAMERON–ERDŐS CONJECTURE

Published online by Cambridge University Press:  19 October 2004

BEN GREEN
BEN GREEN
Affiliation:
Trinity College, Cambridge, Englandbjg23@hermes.cam.ac.uk
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Abstract

A subset $A$ of the integers is said to be sum-free if there do not exist elements $x,y,z \,{\in}\, A$ with $x \,{+}\, y \,{=}\, z$. It is shown that the number of sum-free subsets of $\{1,\ldots,N\}$ is $O(2^{N/2})$, confirming a well-known conjecture of Cameron and Erdős.

Keywords

11B75
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 36 , Issue 6 , November 2004 , pp. 769 - 778
Copyright
© The London Mathematical Society 2004

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Footnotes

Supported by a Fellowship of Trinity College, Cambridge and a grant from the EPSRC, United Kingdom.