{
  "abstract": "Let $\\mathbb{N}_0=\\{0,1,2,\\ldots\\}$ and let $h\\ge2$ be an integer. For a set $A\\subseteq\\mathbb{N}_0$, write $hA$ for the set of all sums of $h$, not necessarily distinct, elements of $A$. In this paper, we prove that for every $h\\ge2$, there is a partition $\\mathbb{N}_0=A\\sqcup B$ such that $A$ is a minimal asymptotic basis of order $h$ and $B$ is a maximal asymptotic nonbasis of order $h$. This solves an open problem posed by Nathanson in 1974.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07361",
  "author_total": 1,
  "authors": [
    {
      "name": "Shi-Qiang Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/en2sed47qesdp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07361",
  "fulltext_url": null,
  "id": "en2sed47qesdp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07361",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7212072494",
  "pdf_url": "https://arxiv.org/pdf/2609.07361",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/en2sed47qesdp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.07361",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07361"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On a problem of Nathanson related to minimal asymptotic bases and maximal asymptotic nonbases",
  "title_text": "On a problem of Nathanson related to minimal asymptotic bases and maximal asymptotic nonbases",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/en2sed47qesdp",
  "venue": "arXiv",
  "versions": []
}