{
  "abstract": "A combinatorial game is a two-player game without hidden information or chance elements. The main object of combinatorial game theory is to determine the outcome (i.e., which player has a winning strategy) of a given position in combinatorial games. Nim is a well-known and fundamental ruleset in combinatorial game theory. This paper proposes a novel partizan variant of Nim called Partizan-Serial-Nim, defined as follows: there are $n$ piles of stones indexed by $1, 2, \\ldots, n$; the two players have permutations $\\mathbfσ^L$ and $\\mathbfσ^R$ of $(1, 2, \\ldots, n)$, respectively; a move is to remove any positive number of stones from the non-empty pile with the minimum value in the player's permutation; the player who cannot make a move loses. This ruleset is a generalization of Serial-Nim and Partizan-End-Nim. We give an algorithm to compute the outcome of a given position in Partizan-Serial-Nim in $O(n^2)$ time, provided that each arithmetic and comparison operation is performed in $O(1)$ time. Also, for the case where all non-empty piles have the same number $m$ of stones, we prove that the outcome does not depend on $m$ for $m \\geq 2$ and present an algorithm to compute the outcome in $O(n)$ time. Further, we prove that the atomic weight of every position in Partizan-Serial-Nim is an integer.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.19876",
  "author_total": 1,
  "authors": [
    {
      "name": "Kengo Hashimoto"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7e2v965yay35w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.19876",
  "fulltext_url": null,
  "id": "7e2v965yay35w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.19876",
  "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": "W7203948463",
  "pdf_url": "https://arxiv.org/pdf/2608.19876",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7e2v965yay35w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.19876",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.19876"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Partizan Serial Nim",
  "title_text": "Partizan Serial Nim",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/7e2v965yay35w",
  "venue": "arXiv",
  "versions": []
}