Forbidden arithmetic progressions in permutations of subsets of the integers

2018/03/15 by Jesse Geneson, Geneson, Jesse
Engineering · Mathematics · Computer Science · #graph theory and CDMA systems #Limits and Structures in Graph Theory #Coding theory and cryptography

paper · pdf · doi:10.48550/arxiv.1803.06334

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 (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.

Related

• Avoiding Monotone Arithmetic Progressions in Permutations of Integers
• On Permutations Avoiding Short Progressions
• A Generalisation of a Result on Monotone Arithmetic Progressions in Permutations of the Positive Integers
• On sets of integers not containing long arithmetic progressions
• On sets of integers which contain no three terms in geometric progression