{
  "abstract": "There are two bijections from unit interval orders on $n$ elements to Dyck paths from $(0,0)$ to $(n,n)$. One is to consider the pairs of incomparable elements as forming the set of boxes between a Dyck path and the diagonal. Another is to find a particular part listing (in the sense of Guay-Paquet, Rowland and Morales) which yields an isomorphic poset, and to interpret the part listing as the area sequence of a Dyck path. Matherne, Morales, and Selover conjectured that, for any unit interval order, these two Dyck paths are related by Haglund's well-known zeta bijection. In this paper we prove their conjecture.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "name": "Félix Gélinas"
    },
    {
      "name": "Adrien Segovia"
    },
    {
      "name": "Hugh Thomas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2r3h0xnjn8ake.bib",
  "cited_by": 0,
  "doi": "10.37236/11825",
  "fulltext_url": null,
  "id": "2r3h0xnjn8ake",
  "issns": [
    "1077-8926"
  ],
  "landing_url": "https://www.combinatorics.org/ojs/index.php/eljc/article/view/v33i4p31",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": "https://www.combinatorics.org/ojs/index.php/eljc/article/download/v33i4p31/pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-06",
  "publisher": "The Electronic Journal of Combinatorics",
  "ris": "https://research.draconitic.com/paper/2r3h0xnjn8ake.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T12:20:56Z",
      "native_id": "10.37236/11825",
      "source": "crossref",
      "url": "https://www.combinatorics.org/ojs/index.php/eljc/article/view/v33i4p31"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:1077-8926",
      "subfield": "combinatorics"
    }
  ],
  "title": "Proof of a Conjecture of Matherne, Morales, and Selover on Encodings of Unit Interval Orders",
  "title_text": "Proof of a Conjecture of Matherne, Morales, and Selover on Encodings of Unit Interval Orders",
  "type": "peer-reviewed",
  "updated_at": "2026-11-08T00:21:33Z",
  "url": "https://research.draconitic.com/paper/2r3h0xnjn8ake",
  "venue": "The Electronic Journal of Combinatorics",
  "versions": []
}