{
  "abstract": "A peeling sequence of a finite planar point set is an ordering of its points, such that when the points get removed in this order, each removed point is a vertex of the current convex hull of the set. Write $g(S)$ for the number of such sequences, and $g(n)$ for the minimum of $g(S)$ over $n$-point sets in general position. We present a method which can be used to prove better upper bounds on the previously analysed recursive 3-block constructions $S_n$. In fact, we prove $g(n)\\leq g(S_n)=O(6.57^n)$, using directional restrictions and a weighted prefix-tree form of the Kraft--McMillan inequality. From the other direction, we show that the same construction cannot attain the current best known lower bound of $c\\cdot3^n$. In fact, $g(S_n)\\geq 5.22^n$ when $n$ is a large enough power of $3$. Improving the general lower bound on $g(n)$ is still an open question.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19540",
  "author_total": 1,
  "authors": [
    {
      "name": "Dániel Gábor Simon"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d8czjt1xhscrb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19540",
  "fulltext_url": null,
  "id": "d8czjt1xhscrb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19540",
  "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"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7213587860",
  "pdf_url": "https://arxiv.org/pdf/2609.19540",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d8czjt1xhscrb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2609.19540",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19540"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Peeling sequences: a directional method for the three-block construction",
  "title_text": "Peeling sequences: a directional method for the three-block construction",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/d8czjt1xhscrb",
  "venue": "arXiv",
  "versions": []
}