{
  "abstract": "Let \\(\\mathcal{B}_n\\) be the Boolean lattice of all subsets of \\([n]\\) and let \\(\\mathcal{P}_{n;\\ell,u}\\) be the subposet of \\(\\mathcal{B}_n\\) induced by the consecutive levels \\(\\ell,\\ell+1,\\ldots,u\\). We determine $ν_{n;\\ell,u}$, the maximum size of a family of pairwise disjoint maximal intervals in $\\mathcal P_{n;\\ell,u}$, whenever \\(u\\le ({n+\\ell^2})/({\\ell+1})\\). This completely settles Engel's problem~[Combin. Probab. Comput., 1996]. The proof is constructive. We also record consequences for weakly cross-intersecting set-pair systems and discuss the three-level case.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.04794",
  "author_total": 2,
  "authors": [
    {
      "name": "Yuxian Dong"
    },
    {
      "name": "Jianxi Mao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e3nfgshm9gz8x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.04794",
  "fulltext_url": null,
  "id": "e3nfgshm9gz8x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.04794",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7167580284",
  "pdf_url": "https://arxiv.org/pdf/2607.04794",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e3nfgshm9gz8x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2607.04794",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.04794"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Engel's Interval Packing Problem in the Boolean Lattice",
  "title_text": "Engel's Interval Packing Problem in the Boolean Lattice",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/e3nfgshm9gz8x",
  "venue": "arXiv",
  "versions": []
}