{
  "abstract": "We construct ternary analogs of dendriform algebras and quadri-algebras, generalizing the well-known binary case. These new structures are defined in terms of nonsymmetric operads. We construct these new operads using ternary operations defined in terms of ternary Rota-Baxter operators. The relations defining these operads lie in the quadratic subspace of the kernel of a rewriting morphism from a free operad to the operad generated by one associative ternary operation and one (or two commuting) unary operators satisfying the ternary Rota-Baxter relation(s). We use computational algebra to compute a basis for the quadratic component of the kernel and thereby obtain the quadratic relations which define these new operads. In the dendriform case, we obtain 3 operations satisfying 10 relations. In the quadri-algebra case, we obtain 9 operations satisfying 50 relations. The latter computations combine modular and rational arithmetic, but we are able to provide certificates of the results which can be verified in characteristic 0.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37848",
  "author_total": 3,
  "authors": [
    {
      "name": "Yu Hin"
    },
    {
      "name": "Au"
    },
    {
      "name": "Murray R. Bremner"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3mkh3d9851xv1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37848",
  "fulltext_url": null,
  "id": "3mkh3d9851xv1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37848",
  "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"
    ],
    [
      "arxiv",
      "math.RA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.37848",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3mkh3d9851xv1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.37848",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37848"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Ternary analogs of dendriform algebras and quadri-algebras",
  "title_text": "Ternary analogs of dendriform algebras and quadri-algebras",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/3mkh3d9851xv1",
  "venue": "arXiv",
  "versions": []
}