Year: 2009
Type: preprint
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.
Source: arXiv (Cornell University)
Author: O'Bryant, Kevin
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2161973946