{
  "abstract": "We say that an antichain in a lattice $L$ is Boolean if it generates a Boolean sublattice in $L$ in a particularly nice way. These purely combinatorial objects play a role in the representation theory of the incidence algebra of the lattice $L$, as indicated by recent results of Rognerud, Yıldırım and of the last author with Klász, Kleinau and Marczinzik. Given these motivations, it is natural to ask: Can we count and construct Boolean antichains in certain lattices? In this paper we give a construction of Boolean antichains in Boolean lattices, partition lattices and Tamari lattices. Furthermore, we share the surprisingly elegant formulas we found for the number of these Boolean antichains.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27126",
  "author_total": 5,
  "authors": [
    {
      "name": "Julien Garber"
    },
    {
      "name": "Lina S. Goltermann"
    },
    {
      "name": "Daniel Horiatakis"
    },
    {
      "name": "Dennis König"
    },
    {
      "name": "Tal Gottesman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0jrn6d8ncr0t7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27126",
  "fulltext_url": null,
  "id": "0jrn6d8ncr0t7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27126",
  "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.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7204586991",
  "pdf_url": "https://arxiv.org/pdf/2608.27126",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0jrn6d8ncr0t7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.27126",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27126"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Counting Boolean Antichains",
  "title_text": "Counting Boolean Antichains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/0jrn6d8ncr0t7",
  "venue": "arXiv",
  "versions": []
}