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On a class of aperiodic sum-free sets

Published online by Cambridge University Press:  24 October 2008

Neil J. Calkin
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, U.S.A e-mail: [email protected]
Paul Erdós
Affiliation:
Hungarian Academy of Sciences, Mathematical Institute, Budapest, Hungary

Abstract

We show that certain natural aperiodic sum-free sets are incomplete, that is that there are infinitely many n not in S which are not a sum of two elements of S.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1996

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References

REFERENCES

[1]Alon, N. and Kleitman, D. J.. Sum-free subsets. In A tribute to Paul Erdös (ed. Baker, A., Bollobás, B. and Hajnal, A.), pp. 1326 (Cambridge University Press, 1990).CrossRefGoogle Scholar
[2]Calkin, Neil J. and Finch, Steven R.. Necessary and sufficient conditions for periodicity of sum-free sets (in preparation).Google Scholar
[3]Calkin, Neil J. and Finch, Steven R.. Difference densities of sum-free sets (in preparation).Google Scholar
[4]Cameron, P. J.. Portrait of a typical sum-free set. In Surveys in Combinatorics 1987 (ed. Whitehead, C.). London Mathematical Society Lecture Notes, 123, pp. 1342 (Cambridge University Press, 1987).Google Scholar
[5]Erdös, P.. Extremal problems in number theory. Proc. Symp. Pure Maths., VIII (1965), 181189.CrossRefGoogle Scholar
[6]Guy, Richard K.. Unsolved problems in number theory (Springer Verlag, 1980).Google Scholar
[7]Hardy, G. H. and Wright, E. M.. An introduction to the theory of numbers (Oxford University Press, 1979).Google Scholar