{
  "abstract": "For every normed space $X$ and integers $1\\le k<n$, we construct a Lipschitz retraction from $X(n)$ onto $X(k)$ with constant at most $2+8n(n-1)$, independently of the dimension of $X$. Here $X(n)$ consists of the nonempty subsets of $X$ with at most $n$ points, equipped with the Hausdorff metric. For the consecutive case $k=n-1$, a separate construction gives the sharper asymptotic bound $O(n\\log n)$. These results extend to barycentric metric spaces and settle some open problems on Lipschitz retractions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31555",
  "author_total": 1,
  "authors": [
    {
      "name": "Leonid V. Kovalev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cwadh9vg1g8vf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31555",
  "fulltext_url": null,
  "id": "cwadh9vg1g8vf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31555",
  "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"
    ],
    [
      "openalex",
      "1702|Advanced Clustering Algorithms Research"
    ]
  ],
  "openalex": "W7223330886",
  "pdf_url": "https://arxiv.org/pdf/2610.31555",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cwadh9vg1g8vf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.31555",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31555"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Lipschitz clustering in normed spaces and barycentric spaces",
  "title_text": "Lipschitz clustering in normed spaces and barycentric spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/cwadh9vg1g8vf",
  "venue": "arXiv",
  "versions": []
}