Thick subsets that do not contain arithmetic progressions
Number Theory
2010-06-25 v3 Combinatorics
Abstract
We adapt the construction of subsets of {1, 2, ..., N} that contain no k-term arithmetic progressions to give a relatively thick subset of an arbitrary set of N integers. Particular examples include a thick subset of {1, 4, 9, ..., N^2} that does not contain a 3-term AP, and a positive relative density subset of a random set (contained in {1, 2, ..., n} and having density c n^{-1/(k-1)}) that is free of k-term APs.
Cite
@article{arxiv.0912.1494,
title = {Thick subsets that do not contain arithmetic progressions},
author = {Kevin O'Bryant},
journal= {arXiv preprint arXiv:0912.1494},
year = {2010}
}
Comments
8 pages; Focus removed from APs of primes, put on thinner sets