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Irregular sets of integers generated by the greedy algorithm


Author: Joseph L. Gerver
Journal: Math. Comp. 40 (1983), 667-676
MSC: Primary 10L20; Secondary 10H20
DOI: https://doi.org/10.1090/S0025-5718-1983-0689480-2
MathSciNet review: 689480
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Abstract: The greedy algorithm was used to generate sets of positive integers containing no subset of the form $ \{ x,x + y,x + 2y\} $, $ \{ x,x + y,x + 3y\} $, $ \{ x,x + 2y,x + 3y\} $, $ \{ x,x + 3y,x + 4y\} $, $ \{ x,x + 3y,x + 5y\} $, and $ \{ x,x + y,x + 2y,x + 3y\} $, respectively. All of these sets have peaks of density in roughly geometric progression.


References [Enhancements On Off] (What's this?)

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  • [3] J. L. Gerver & L. T. Ramsey, "Sets of integers with no long arithmetic progressions generated by the greedy algorithm," Math. Comp., v. 33, 1979, pp. 1353-1359. MR 537982 (80k:10053)
  • [4] A. M. Odlyzko & R. P. Stanley, "Some curious sequences constructed with the greedy algorithm," unpublished Bell Laboratories report, January 1978.
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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1983-0689480-2
Article copyright: © Copyright 1983 American Mathematical Society

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