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arXiv · 1803.06334

Forbidden arithmetic progressions in permutations of subsets of the integers

Jesse Geneson
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Abstract

Permutations of the positive integers avoiding arithmetic progressions of length $5$ were constructed in (Davis et al, 1977), implying the existence of permutations of the integers avoiding arithmetic progressions of length $7$. We construct a permutation of the integers avoiding arithmetic progressions of length $6$. We also prove a lower bound of $\frac{1}{2}$ on the lower density of subsets of positive integers that can be permuted to avoid arithmetic progressions of length $4$, sharpening the lower bound of $\frac{1}{3}$ from (LeSaulnier and Vijay, 2011). In addition, we generalize several results about forbidden arithmetic progressions to construct permutations avoiding generalized arithmetic progressions.

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Jesse Geneson. 2018-03-15. Forbidden arithmetic progressions in permutations of subsets of the integers. https://arxiv.org/abs/1803.06334

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