{
  "abstract": "Let $m\\geq1$ be an integer and let $W=(m\\mathbb N_0+X)\\cup U\\cup V\\subseteq\\mathbb Z$ be bounded below, where $X\\ne\\varnothing$, $[U]_m\\subseteq[X]_m$, $[X]_m\\cap[V]_m=\\varnothing$, and $V$ contains no infinite arithmetic progression with common difference $m$. Here $[S]_m$ denotes the set of residue classes modulo $m$ represented by $S$. Suppose that $W$ satisfies the $\\mathcal C$-condition modulo $m$. For $0\\leq r<m$, let $V_r=V\\cap(r+m\\mathbb Z)$, and put $V'=\\bigcup_{|V_r|=\\infty}V_r$, where the union is over $0\\leq r<m$. We prove that $W$ has a minimal additive complement if $V'$ satisfies the big-hole property modulo $m$. This answers a problem posed by Ma and Chen.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26608",
  "author_total": 2,
  "authors": [
    {
      "name": "Shi-Qiang Chen"
    },
    {
      "name": "Quan-Hui Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4a2vvakfndnkq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26608",
  "fulltext_url": null,
  "id": "4a2vvakfndnkq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26608",
  "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"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7223069033",
  "pdf_url": "https://arxiv.org/pdf/2610.26608",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4a2vvakfndnkq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.26608",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26608"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On a problem of Ma and Chen concerning minimal additive complements",
  "title_text": "On a problem of Ma and Chen concerning minimal additive complements",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/4a2vvakfndnkq",
  "venue": "arXiv",
  "versions": []
}