{
  "abstract": "Let $L$ be a thin distributive lattice of rank $m+1$, and let $I_L$ be its join-meet ideal in the polynomial ring $S_L$. For $A\\subseteq\\{1,\\dots,m\\}$, let $J_A$ be the ideal obtained from $I_L$ by identifying, for every $i\\in A$, the variables of the two elements of $L$ of rank $i$. We prove that $J_A$ is prime if and only if $A$ contains no turning rank and does not contain both ranks adjacent to a turning rank. In this case, $S_L/J_A$ is the toric ring obtained from Hibi's parametrization of the Hibi ring of $L$ by identifying suitable pairs of variables, and for an arbitrary $A$ we describe the saturation of $J_A$ as a lattice ideal.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32647",
  "author_total": 3,
  "authors": [
    {
      "name": "Takayuki Hibi"
    },
    {
      "name": "Francesco Navarra"
    },
    {
      "name": "Ayesha Asloob Qureshi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4h7934tcvg9tw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32647",
  "fulltext_url": null,
  "id": "4h7934tcvg9tw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32647",
  "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.AC"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7223691936",
  "pdf_url": "https://arxiv.org/pdf/2610.32647",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4h7934tcvg9tw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32647",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32647"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Rank identifications in join-meet ideals of thin distributive lattices",
  "title_text": "Rank identifications in join-meet ideals of thin distributive lattices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/4h7934tcvg9tw",
  "venue": "arXiv",
  "versions": []
}