Forbidden arithmetic progressions in permutations of subsets of the integers

03/15/2018

∙

by   Jesse Geneson, et al.

∙

0

∙

share

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 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 1/3 from (LeSaulnier and Vijay, 2011). In addition, we generalize several results about forbidden arithmetic progressions to construct permutations avoiding generalized arithmetic progressions.