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Mathematics of Computation

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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
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.

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Article copyright: © Copyright 1983 American Mathematical Society