{
  "abstract": "Sierksma's conjecture asserts that every affine map $a\\colonΔ_{(d+1)(r-1)}\\longrightarrow\\mathbb{R}^d$ has at least $((r-1)!)^d$ unordered Tverberg partitions into $r$ parts. Until now, lower bounds growing with $d$ were known only when $r$ is a prime power. As one of our main results we prove that for every integer $r\\geq3$, every decomposition $r=kq+s$ into $q=p^α$ a prime power, $k\\geq1$ and $s\\geq0$, and every affine map $a$, the number $\\operatorname{Tv}(a)$ of unordered Tverberg partitions satisfies \\[ \\operatorname{Tv}(a)\\ \\geq\\ \\frac{q}{r!}\\,\\Big(\\frac{q}{α+1}\\Big)^{\\big\\lceil\\frac{(r-1-2s)(d+1)}{2}\\big\\rceil}. \\]",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32086",
  "author_total": 2,
  "authors": [
    {
      "name": "Matija Blagojević"
    },
    {
      "name": "Pavle V. M. Blagojević"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9mkjc642vk7vn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32086",
  "fulltext_url": null,
  "id": "9mkjc642vk7vn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32086",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AT"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7223703292",
  "pdf_url": "https://arxiv.org/pdf/2610.32086",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9mkjc642vk7vn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32086",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32086"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The number of Tverberg partitions beyond prime powers",
  "title_text": "The number of Tverberg partitions beyond prime powers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/9mkjc642vk7vn",
  "venue": "arXiv",
  "versions": []
}