Almost disjoint families of 3-term arithmetic progressions

摘要

We obtain upper and lower bounds for the size of a largest family of 3-term arithmetic progressions contained in [0, n - 1], no two of which intersect in more than one point. Such a family consists of just under a half of all of the 3-term arithmetic progressions contained in [0, n - 1]. (C) 2004 Elsevier Inc. All rights reserved.