{
  "abstract": "We deal with the following two pick-up sticks problems: given an integer n greater than or equal to 3, we choose n sticks with independent random lengths from an exponential distribution or Pareto type I distribution, and we are interested in the probability that no three of them can be the sides of a triangle. In case of exponential distribution, this problem has been solved by other authors: the probability in question is equal to $n!/\\big((F_3-1)(F_4-1)\\cdots(F_{n+2}-1)\\big)$, where $(F_i)_{i=1}^\\infty$ is the sequence of Fibonacci numbers. We give a new, self-contained and detailed proof for this formula, which uses a different method compared to the earlier ones. In case of Pareto type I distribution, we derive new formulae for the corresponding probability.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04436",
  "author_total": 2,
  "authors": [
    {
      "name": "Matyas Barczy"
    },
    {
      "name": "Rezső Lovas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6v8j08vxftz2y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04436",
  "fulltext_url": null,
  "id": "6v8j08vxftz2y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04436",
  "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.MG"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04436",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6v8j08vxftz2y.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04436",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04436"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Pick-up sticks problems for exponential and Pareto distributions",
  "title_text": "Pick-up sticks problems for exponential and Pareto distributions",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/6v8j08vxftz2y",
  "venue": "arXiv",
  "versions": []
}