The Number of Subsets of Integers with No<i>k</i>-Term Arithmetic Progression
The Number of Subsets of Integers with No<i>k</i>-Term Arithmetic Progression
Addressing a question of Cameron and Erdős, we show that, for infinitely many values of n, the number of subsets of {1,2,…,n} that do not contain a k-term arithmetic progression is at most 2O(rk(n)), where rk(n) is the maximum cardinality of a subset of {1,2,…,n} without a k-term arithmetic progression. …