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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the number of maximal sum-free sets


Authors: Tomasz Luczak and Tomasz Schoen
Journal: Proc. Amer. Math. Soc. 129 (2001), 2205-2207
MSC (2000): Primary 11B75; Secondary 05A16
Published electronically: December 28, 2000
MathSciNet review: 1823901
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Abstract:

It is shown that the set $\{1,2,\dots,n\}$ contains at most $2^{n/2-2^{-28}n}$ maximal sum-free subsets, provided $n$ is large enough.


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Additional Information

Tomasz Luczak
Affiliation: Department of Discrete Mathematics, Adam Mickiewicz University, ul. Matejki 48/49, 60-769 Poznań, Poland
Email: tomasz@amu.edu.pl

Tomasz Schoen
Affiliation: Mathematisches Seminar, Universität zu Kiel, Ludewig-Meyn-Str. 4, 24098 Kiel, Germany – Department of Discrete Mathematics, Adam Mickiewicz University, ul. Matejki 48/49, 60-769 Poznań, Poland
Email: tos@numerik.uni-kiel.de

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05815-9
PII: S 0002-9939(00)05815-9
Received by editor(s): September 7, 1999
Received by editor(s) in revised form: December 13, 1999
Published electronically: December 28, 2000
Additional Notes: The first author was supported in part by KBN Grant 2 P03A 021 17.
Communicated by: John R. Stembridge
Article copyright: © Copyright 2000 American Mathematical Society