On B_h[1]-sets which are asymptotic bases of order 2h

2022/02/28 by Kiss, Sándor Z., Sándor, Csaba
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2202.13841

Abstract

Let h,k ≥ 2 be integers. A set A of positive integers is called asymptotic basis of order k if every large enough positive integer can be written as the sum of k terms from A. A set of positive integers A is said to be a B_h[g]-set if every positive integer can be written as the sum of h terms from A at most g different ways. In this paper we prove the existence of B_h[1] sets which are asymptotic bases of order 2h by using probabilistic methods.

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