Generalized asymptotic Sidon basis

2019/09/04 by Kiss, Sándor Z., Sándor, Csaba
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1909.01714

Abstract

Let h,k ≥ 2 be integers. We say a set A of positive integers is an asymptotic basis of order k if every large enough positive integer can be represented as the sum of k terms from A. A set of positive integers A is called B_h[g] set if all positive integers can be represented as the sum of h terms from A at most g times. In this paper we prove the existence of B_h[1] sets which are asymptotic bases of order 2h+1 by using probabilistic methods.

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