{
  "abstract": "We prove continuity for reflexive, bisymmetric binary operations that are strictly increasing in each variable, under certain algebraic conditions. In fact, for some algebraic weights we construct a weighted quasi-arithmetic representation of such functions without assuming continuity. An elementary construction gives the case $r=2/3$. More generally, a word equality whose polynomial difference has a unique simple zero $r\\in(0,1)$ forces the representation with weight $r$; every algebraic $r$ with no other conjugate in $(0,1)$ arises this way. The proof uses an affine embedding and a dense-domain extension argument.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.10021",
  "author_total": 3,
  "authors": [
    {
      "name": "Pál Burai"
    },
    {
      "name": "Gergely Kiss"
    },
    {
      "name": "Patricia Szokol"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8743cdsv8h8td.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.10021",
  "fulltext_url": null,
  "id": "8743cdsv8h8td",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.10021",
  "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.GM"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.10021",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8743cdsv8h8td.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T06:21:33Z",
      "native_id": "2611.10021",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.10021"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GM",
      "subfield": "general"
    }
  ],
  "title": "Constructive algebraic methods for bisymmetric means",
  "title_text": "Constructive algebraic methods for bisymmetric means",
  "type": "preprint",
  "updated_at": "2026-11-10T06:21:33Z",
  "url": "https://research.draconitic.com/paper/8743cdsv8h8td",
  "venue": "arXiv",
  "versions": []
}