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A new class of minimal asymptotic bases

Number Theory 2022-12-14 v2 Combinatorics

Abstract

A set AA of nonnegative integers is an asymptotic basis of order hh if every sufficiently large integer can be represented as the sum of hh not necessarily distinct elements of AA. The asymptotic basis AA is minimal if removing any element of AA destroys every representation of infinitely many integers, and so A{a}A\setminus \{a\} is not an asymptotic basis of order hh for all aAa\in A. In this paper, a new class of minimal asymptotic bases is constructed.

Keywords

Cite

@article{arxiv.2006.14562,
  title  = {A new class of minimal asymptotic bases},
  author = {Melvyn B. Nathanson},
  journal= {arXiv preprint arXiv:2006.14562},
  year   = {2022}
}

Comments

10 pages; minor improvements and corrections