Title:
Some Conditions on Periodicity for Sum-Free Sets
Some Conditions on Periodicity for Sum-Free Sets
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Author(s)
Calkin, Neil J.
Finch, Steven R.
Finch, Steven R.
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Abstract
Cameron has introduced a natural bijection between the set of one way in nite binary sequences and
the set of sum-free sets (of positive integers), and observed that a sum-free set is ultimately periodic only
if the corresponding binary sequence is ultimately periodic. He asked if the converse also holds. In this
paper we present 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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Date Issued
1995-07
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Text
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Pre-print