{
  "abstract": "For every overlap $m\\geq 3$ and every pattern length $K\\geq 2m+1$, we construct an explicit permutation $p\\in\\mathfrak{S}_K$ such that the number of permutations containing $j$ prescribed occurrences of $p$, with successive starts separated by $K-m$, is $(2j-1)!!$ for every $j\\geq 1$. Additional occurrences are permitted. We prove that the corresponding occurrence poset is the ordinal sum of a chain on $m+j(K-m-2)$ elements and a comb on $2j$ elements. An insertion bijection counts the linear extensions of the comb. This gives the uniform representatives requested in the double-factorial part of Question 6 in Section 7 of Blitvić, Kammoun and Steingrímsson, arXiv:2610.29846v1. A Lean 4 formalization and its recorded verification data accompany the paper.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06937",
  "author_total": 1,
  "authors": [
    {
      "name": "Zoltán Nagy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ec2v6nm57dddj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06937",
  "fulltext_url": null,
  "id": "ec2v6nm57dddj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06937",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06937",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ec2v6nm57dddj.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.06937",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06937"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A uniform double-factorial construction for consecutive-pattern packings",
  "title_text": "A uniform double-factorial construction for consecutive-pattern packings",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:46Z",
  "url": "https://research.draconitic.com/paper/ec2v6nm57dddj",
  "venue": "arXiv",
  "versions": []
}