Irregular sets of integers generated by the greedy algorithm

Gerver, Joseph L.

doi:10.1090/S0025-5718-1983-0689480-2

Irregular sets of integers generated by the greedy algorithm
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by Joseph L. Gerver PDF

Math. Comp. 40 (1983), 667-676 Request permission

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

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