Forbidden arithmetic progressions in permutations of subsets of the integers
نویسنده
چکیده
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 13 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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تاریخ انتشار 2018