{
  "abstract": "We study pairs of labeled random partitions $(Π,τ)$ with a finite label set $E$, which can be thought of as a random mutation and coalescence mechanism of a countable number of blocks. Labeled exchangeable partition probability functions (LEPPFs) are defined via labeled analogues of Kingman's paintbox partitions. They satisfy normalization, symmetry and consistency in a multivariate sense. Under an equivariance condition, a representation for $(Π,τ)$ in terms of labeled paintbox partitions is derived, leading to a full characterization of LEPPFs by a unique probability measure $G$. This representation is extended to jointly exchangeable and consistent transition pairs using a product measure $F \\otimes G$. These results yield a one-to-one correspondence between distributions of jointly exchangeable and consistent transition pairs and pairs of exchangeable distributions and LEPPFs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29824",
  "author_total": 2,
  "authors": [
    {
      "name": "Maximilian Flamm"
    },
    {
      "name": "Martin Möhle"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/965b5jtq48m7y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29824",
  "fulltext_url": null,
  "id": "965b5jtq48m7y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29824",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7223232227",
  "pdf_url": "https://arxiv.org/pdf/2610.29824",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/965b5jtq48m7y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.29824",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29824"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "A paintbox characterization of labeled partitions",
  "title_text": "A paintbox characterization of labeled partitions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/965b5jtq48m7y",
  "venue": "arXiv",
  "versions": []
}