{
  "id": "2108.07680",
  "version": "v1",
  "published": "2021-08-17T15:28:34.000Z",
  "updated": "2021-08-17T15:28:34.000Z",
  "title": "Counterexamples to the Colorful Tverberg Conjecture for Hyperplanes",
  "authors": [
    "João Pedro Carvalho",
    "Pablo Soberón"
  ],
  "comment": "5 pagse, 1 figure",
  "categories": [
    "math.CO"
  ],
  "abstract": "In 2008 Karasev conjectured that for every set of $r$ blue lines, $r$ green lines, and $r$ red lines in the plane, there exists a partition of them into $r$ colorful triples whose induced triangles intersect. We disprove this conjecture for every $r$ and extend the counterexamples to higher dimensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-17T15:28:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "colorful tverberg conjecture",
      "counterexamples",
      "hyperplanes",
      "green lines",
      "higher dimensions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}