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On the number of maximal sum-free sets

Author(s): Tomasz Luczak; Tomasz Schoen
Journal: Proc. Amer. Math. Soc. 129 (2001), 2205-2207.
MSC (2000): Primary 11B75; Secondary 05A16
Posted: December 28, 2000
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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 is large enough.

References:

1.: N. Alon, Independent sets in regular graphs and sum-free subsets of finite groups, Israel J. Math 73 (1991), 247-256. MR 92k:11024
2.: N. Calkin, On the number of sum-free sets, Bull. London Math. Soc. 22 (1990) 141-144. MR 91b:11015
3.: P. Cameron, Portrait of a typical sum-free set. In ``Survey in Combinatorics 1987'' (C. Whitehead, ed.), London Mathematical Lecture Note Ser. 123, Cambridge University Press, 1987, 13-42. MR 88k:05138
4.: P. Cameron and P. Erdos, On the number of sets of integers with various properties. In ``Number Theory: Proc. First Conf. Can. Number Th. Ass.'' (R.A. Mollin, ed.), Banff, 1988, de Gruyter, 1990, 61-79. MR 92g:11010

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Additional Information:

Tomasz Luczak
Affiliation: Department of Discrete Mathematics, Adam Mickiewicz University, ul. Matejki 48/49, 60-769 Poznan, 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 Poznan, Poland
Email: tos@numerik.uni-kiel.de

DOI: 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
Posted: December 28, 2000
Additional Notes: The first author was supported in part by KBN Grant 2 P03A 021 17.
Communicated by: John R. Stembridge
Copyright of article: Copyright 2000, American Mathematical Society


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