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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Greedily partitioning the natural numbers into sets free of arithmetic progressions


Authors: Joseph Gerver, James Propp and Jamie Simpson
Journal: Proc. Amer. Math. Soc. 102 (1988), 765-772
MSC: Primary 11B25; Secondary 05A99
MathSciNet review: 929018
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Abstract: We describe a "greedy" algorithm for partitioning the natural numbers into sets free of arithmetic progressions of length 3. A recursive formula governing the resulting partition is proved, and some features of its asymptotic behavior are discussed.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0929018-1
PII: S 0002-9939(1988)0929018-1
Article copyright: © Copyright 1988 American Mathematical Society