On asymptotic bases and minimal asymptotic bases
Volume 170 / 2022
Colloquium Mathematicum 170 (2022), 65-77
MSC: Primary 11B13.
DOI: 10.4064/cm8321-9-2021
Published online: 20 April 2022
Abstract
Let and A\subset \mathbb {N}. Let h\geq 2 and let r_h(A,n)=\sharp \{ (a_1,\ldots ,a_h) \in A^{h}: a_1+\cdots +a_h=n\}. The set A is called an asymptotic basis of order h if r_h(A,n)\geq 1 for all sufficiently large integers n. An asymptotic basis A of order h is minimal if no proper subset of A is an asymptotic basis of order h. Recently, Chen and Tang resolved a problem of Nathanson on minimal asymptotic bases of order h. In this paper, we generalize this result to g-adic representations.
