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1996 Conditions on periodicity for sum-free sets
Neil J. Calkin, Steven R. Finch
Experiment. Math. 5(2): 131-137 (1996).

Abstract

Cameron has introduced a natural one-to-one correspondence between infinite binary sequences and sets of positive integers with the property that no two elements add up to a third. He observed that, if a sum-free set is ultimately periodic, so is the corresponding binary sequence, and asked if the converse also holds. We present here necessary and sufficient conditions for a sum-free set to be ultimately periodic, and show how these conditions can be used to test specific sets. These tests produce the first evidence of a positive nature that certain sets are, in fact, not ultimately periodic.

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Neil J. Calkin. Steven R. Finch. "Conditions on periodicity for sum-free sets." Experiment. Math. 5 (2) 131 - 137, 1996.

Information

Published: 1996
First available in Project Euclid: 13 March 2003

zbMATH: 0871.11013
MathSciNet: MR1418960

Subjects:
Primary: 11B13
Secondary: 11B75

Rights: Copyright © 1996 A K Peters, Ltd.

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Vol.5 • No. 2 • 1996
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