On asymptotic bases and minimal asymptotic bases

2018/10/25 by Tang, Min, Ling, Deng-Rong
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1810.10925

Abstract

Let ℕ denote the set of all nonnegative integers and A be a subset of ℕ. Let h≥2 and let r_h(A,n)=\sharp \ (a₁,…,a_h)∈ A^h: a₁+⋯+a_h=n\. The set A is called an asymptotic basis of order h if r_h(A,n)≥ 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 resoved a problem of Nathanson on minimal asymptotic bases of order h. In this paper, we generalized this result to g-adic representations.

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