Shatrovskii's construction of thin bases

Abstract

The set A of nonnegative integers is called a basis of order h if every nonnegative integer can be represented as the sum of exactly h not necessarily distinct elements of A. An additive basis A of order h is called thin if there exists c > 0 such that the number of elements of A not exceeding x is less than cx^{1/h} for all x > 0. This paper describes a construction of Shatrovskii of thin bases of order h.