Generalized asymptotic Sidon basis

Kiss, Sándor and Sándor, Csaba (2021) Generalized asymptotic Sidon basis. DISCRETE MATHEMATICS, 344 (2). ISSN 0012-365X

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Abstract

Let $h,k \ge 2$ 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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