Thick subsets that do not contain arithmetic progressions

Details Thick subsets that do not contain arithmetic progressions Thick subsets that do not contain arithmetic progressions

2009-12-08

arxiv.org/abs/0912.1494v3

Mathematics

Number Theory

8 pages; Focus removed from APs of primes, put on thinner sets

Scientific paper

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.

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