Thin bases in additive number theory

https://doi.org/10.1016/j.disc.2012.03.026Get rights and content
Under an Elsevier user license
open archive

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 cx1/h for all x1. This paper describes a construction of Shatrovskii˘ of thin bases of order h.

Keywords

Additive number theory
Thin bases
Bases of finite order
Shatrovskii˘ bases

Cited by (0)