{
  "abstract": "Let $g>h\\ge2$ be integers. For a nonempty set $W\\subseteq\\N$, let $\\mathcal F^*(W)$ denote the set of its finite nonempty subsets. Let $$A_g(W)=\\left\\{\\sum_{f\\in F}a_fg^f: 1\\leq a_f \\leq g-1,F \\in \\mathcal F^*(W)\\right\\},$$ and let $\\N=W_1\\sqcup\\cdots\\sqcup W_h$ be a partition into infinite sets. We prove that $A=\\bigcup_{i=1}^h A_g(W_i)$ is a minimal asymptotic basis of order $h$ for every such partition.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23152",
  "author_total": 1,
  "authors": [
    {
      "name": "Min Tang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6xdbar21xhj4z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23152",
  "fulltext_url": null,
  "id": "6xdbar21xhj4z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23152",
  "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": "W7222923930",
  "pdf_url": "https://arxiv.org/pdf/2610.23152",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6xdbar21xhj4z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23152",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23152"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Minimal asymptotic \\(g\\)-adic bases from arbitrary partitions",
  "title_text": "Minimal asymptotic g-adic bases from arbitrary partitions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/6xdbar21xhj4z",
  "venue": "arXiv",
  "versions": []
}