{
  "abstract": "It is well known that the polymorphism clone of a quasiorder is determined by its unary part, in the sense that any operation is a polymorphism if it satisfies the condition that all unary functions obtained by fixing some of its variables at constant values are polymorphisms. We show that a clone satisfies an analogous property for a particular fixed arity $d$ if and only if it is determined by a collection of what we call higher-dimensional generalized quasiorders whose dimension is equal to $d$. We define higher-dimensional generalized quasiorders with the appropriate generalizations of reflexivity and transitivity to the higher-dimensional setting, which rely on an explicit analysis of 'rectangular' arity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07339",
  "author_total": 2,
  "authors": [
    {
      "name": "Andrew Moorhead"
    },
    {
      "name": "Reinhard Pöschel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8203dskzd3g1h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07339",
  "fulltext_url": null,
  "id": "8203dskzd3g1h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07339",
  "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.LO"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "1703|Advanced Algebra and Logic"
    ]
  ],
  "openalex": "W7212019667",
  "pdf_url": "https://arxiv.org/pdf/2609.07339",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8203dskzd3g1h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.07339",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07339"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Higher-dimensional generalized quasiorders",
  "title_text": "Higher-dimensional generalized quasiorders",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/8203dskzd3g1h",
  "venue": "arXiv",
  "versions": []
}