{
  "abstract": "This paper studies the longest increasing subsequence (LIS) problem for sequences generated by dyadic-type chaotic interval maps. Starting from a single point $x\\in[0,1)$ chosen uniformly at random, we form the order pattern of the first $N$ points of its orbit, with the doubling map as the basic model. Let $λ_1^{(N)}$ be the LIS length, equivalently the length of the first row of the Young diagram obtained by Schensted's insertion. We show that $\\mathbb E[λ_1^{(N)}]/\\sqrt N\\to 2$, matching the leading asymptotics in the classical Ulam--Hammersley problem for uniform random permutations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.24575",
  "author_total": 3,
  "authors": [
    {
      "name": "Shinsuke Iwao"
    },
    {
      "name": "Fumihiko Nakamura"
    },
    {
      "name": "Yushi Nakano"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0as1z6z9pnkg1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.24575",
  "fulltext_url": null,
  "id": "0as1z6z9pnkg1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.24575",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7204235592",
  "pdf_url": "https://arxiv.org/pdf/2608.24575",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0as1z6z9pnkg1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2608.24575",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.24575"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Longest increasing subsequences of dyadic-type chaotic orbits",
  "title_text": "Longest increasing subsequences of dyadic-type chaotic orbits",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/0as1z6z9pnkg1",
  "venue": "arXiv",
  "versions": []
}