{
  "abstract": "We prove the Bárány--Kalai--Tverberg conjecture extending the affine version of Tverberg's theorem to simplicial balls and polytopes other than the simplex: For any affine map $ϕ: P\\to \\mathbb R^d$ from a convex polytope $P$ of dimension $N=(d+1)(r-1)$ with $r\\geq 2$, there exist $r$ pairwise disjoint faces $F_1,\\ldots,F_r\\subset\\partial P$ such that $ϕ(F_1)\\cap\\dots\\capϕ(F_r)\\neq\\varnothing$. A similar statement holds for a simplicial ball $P$ with $ϕ$ assumed affine on all of its faces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12483",
  "author_total": 2,
  "authors": [
    {
      "name": "Sergey Avvakumov"
    },
    {
      "name": "Roman Karasev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/drh1btjshjnf1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12483",
  "fulltext_url": null,
  "id": "drh1btjshjnf1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12483",
  "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.CO"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7213203578",
  "pdf_url": "https://arxiv.org/pdf/2609.12483",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/drh1btjshjnf1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.12483",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12483"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The affine Tverberg theorem revisited",
  "title_text": "The affine Tverberg theorem revisited",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/drh1btjshjnf1",
  "venue": "arXiv",
  "versions": []
}