{
  "abstract": "In this paper, we provide a complete description of the preperiods, periodic lengths, and the Grundy-value sequences of two-element subtraction games with a single pass option.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25829",
  "author_total": 1,
  "authors": [
    {
      "name": "Richard M. Low"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6s42gw81m5xet.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25829",
  "fulltext_url": null,
  "id": "6s42gw81m5xet",
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  "landing_url": "https://arxiv.org/abs/2610.25829",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
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      "openalex",
      "2607|Advanced Combinatorial Mathematics"
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  "openalex": "W7222998913",
  "pdf_url": "https://arxiv.org/pdf/2610.25829",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6s42gw81m5xet.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25829",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25829"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A classification of the Nim-sequences for the two-element subtraction game with a single pass",
  "title_text": "A classification of the Nim-sequences for the two-element subtraction game with a single pass",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/6s42gw81m5xet",
  "venue": "arXiv",
  "versions": []
}