{
  "abstract": "We study tropical friezes and cluster-additive functions associated to symmetrizable generalized Cartan matrices in the framework of Fock-Goncharov duality in cluster algebras. In particular, we generalize and prove a conjecture of C. M. Ringel on cluster-additive functions associated to arbitrary Cartan matrices of finite type. For a Fock-Goncharov dual pair of positive spaces of finite type, we use tropical friezes and cluster-additive functions to explicitly express the Fock-Goncharov pairing between their tropical points and the bijections between global monomials on one and tropical points of the other.",
  "abstract_shown": true,
  "affiliations": [
    "University of Science and Technology of China",
    "The University of Hong Kong"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Peigen Cao",
      "orcid": "0000-0002-2994-8589"
    },
    {
      "affs": [
        1
      ],
      "name": "Antoine de Saint Germain",
      "orcid": "0009-0001-7958-2343"
    },
    {
      "affs": [
        1
      ],
      "name": "Jiang-Hua Lu",
      "orcid": "0000-0002-4366-1568"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/84p0szgz8p7zp.bib",
  "cited_by": 1,
  "doi": "10.1017/fms.2026.10291",
  "fulltext_url": null,
  "id": "84p0szgz8p7zp",
  "issns": [
    "2050-5094"
  ],
  "landing_url": "https://www.cambridge.org/core/product/identifier/S2050509426102916/type/journal_article",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W4389217888",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": "Cambridge University Press (CUP)",
  "ris": "https://research.draconitic.com/paper/84p0szgz8p7zp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "10.1017/fms.2026.10291",
      "source": "crossref",
      "url": "https://www.cambridge.org/core/product/identifier/S2050509426102916/type/journal_article"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2608|Algebraic structures and combinatorial models",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Tropical friezes and cluster-additive functions via Fock-Goncharov duality and a conjecture of Ringel",
  "title_text": "Tropical friezes and cluster-additive functions via Fock-Goncharov duality and a conjecture of Ringel",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/84p0szgz8p7zp",
  "venue": "Forum of Mathematics, Sigma",
  "versions": []
}