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 | References | Similar Articles | Additional Information

It is shown that the set contains at most maximal sum-free subsets, provided is large enough.

**1.**Noga Alon,*Independent sets in regular graphs and sum-free subsets of finite groups*, Israel J. Math.**73**(1991), no. 2, 247–256. MR**1135215**, 10.1007/BF02772952**2.**Neil J. Calkin,*On the number of sum-free sets*, Bull. London Math. Soc.**22**(1990), no. 2, 141–144. MR**1045283**, 10.1112/blms/22.2.141**3.**P. J. Cameron,*Portrait of a typical sum-free set*, Surveys in combinatorics 1987 (New Cross, 1987) London Math. Soc. Lecture Note Ser., vol. 123, Cambridge Univ. Press, Cambridge, 1987, pp. 13–42. MR**905274****4.**P. J. Cameron and P. Erdős,*On the number of sets of integers with various properties*, Number theory (Banff, AB, 1988) de Gruyter, Berlin, 1990, pp. 61–79. MR**1106651**

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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:
https://doi.org/10.1090/S0002-9939-00-05815-9

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