{
  "abstract": "We consider a variant of Nim in which, for a fixed set $S$ of nonnegative integers, a move is forbidden if the total number of remaining stones belongs to $S$. This game coincides with normal-play Nim when $S=\\emptyset$, and with misère Nim when $S=\\{0\\}$. In this paper, we focus in particular on the case where $S$ is the set of multiples of $d$, and show that simple criteria for determining the outcome can be obtained for $d=2,3,4$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.11665",
  "author_total": 2,
  "authors": [
    {
      "name": "Hiromi Oginuma"
    },
    {
      "name": "Masato Shinoda"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7a5ans16p02nw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.11665",
  "fulltext_url": null,
  "id": "7a5ans16p02nw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.11665",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7202343039",
  "pdf_url": "https://arxiv.org/pdf/2608.11665",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7a5ans16p02nw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2608.11665",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.11665"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Forbidden-Total-Size Nim",
  "title_text": "Forbidden-Total-Size Nim",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/7a5ans16p02nw",
  "venue": "arXiv",
  "versions": []
}