Thick subsets that do not contain arithmetic progressions

2009/12/08 by O'Bryant, Kevin
#11B25 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.0912.1494

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, ..., N² 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.

Related

• On sets of integers not containing long arithmetic progressions
• Small subsets without k-term arithmetic progressions
• Sets of integers that do not contain long arithmetic progressions
• The number of subsets of integers with no k-term arithmetic progression
• Four-term progression free sets with three-term progressions in all\n large subsets