{
  "abstract": "Let $h\\geq2$ be an integer and let $\\mathbb{N}_0=W_1\\cup\\cdots\\cup W_h$ be a partition into infinite sets. For $W\\subseteq\\mathbb{N}_0$, let $A(W)$ denote the set of all finite nonempty sums of distinct powers $2^w$ with $w\\in W$. We give a necessary and sufficient condition for $A=A(W_1)\\cup\\cdots\\cup A(W_h)$ to be a strongly minimal asymptotic basis of order $h$. This provides a complete answer to a problem posed by Nathanson in 1988.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15416",
  "author_total": 2,
  "authors": [
    {
      "name": "Shi-Qiang Chen"
    },
    {
      "name": "Xin-Yue Yan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7antja91p5vy0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15416",
  "fulltext_url": null,
  "id": "7antja91p5vy0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15416",
  "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.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7221772143",
  "pdf_url": "https://arxiv.org/pdf/2610.15416",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7antja91p5vy0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15416",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15416"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On strongly minimal asymptotic bases of order $h$ generated by powers of $2$",
  "title_text": "On strongly minimal asymptotic bases of order h generated by powers of $2$",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/7antja91p5vy0",
  "venue": "arXiv",
  "versions": []
}