{
  "abstract": "A crescent configuration of $n$ points in $\\mathbb R^d$ is a set in general position whose distinct pairwise distances have multiplicities $1,\\ldots,n-1$. We construct such a configuration in $\\mathbb R^3$ for every $n\\geq3$, giving a uniform bound of three for the minimum dimension. The proof uses equally spaced parameters on a short circular helix and Rolle's theorem. We also give explicit integer-coordinate configurations with $O(n\\log n)$ bits per coordinate, and prove that every finite initial segment of the sequence $(\\cos j,\\sin j,2j)_{j\\geq0}$ of length at least three is a crescent configuration.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38368",
  "author_total": 1,
  "authors": [
    {
      "name": "Yuda Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9e9120zq0412e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38368",
  "fulltext_url": null,
  "id": "9e9120zq0412e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38368",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38368",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9e9120zq0412e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38368",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38368"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Crescent configurations in three dimensions",
  "title_text": "Crescent configurations in three dimensions",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/9e9120zq0412e",
  "venue": "arXiv",
  "versions": []
}