{
  "id": "1412.6639",
  "version": "v1",
  "published": "2014-12-20T10:40:47.000Z",
  "updated": "2014-12-20T10:40:47.000Z",
  "title": "A geometric Hall-type theorem",
  "authors": [
    "Andreas Holmsen",
    "Leonardo Martinez-Sandoval",
    "Luis Montejano"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We introduce a geometric generalization of Hall's marriage theorem. Given a family $F = \\{X_1, \\dots, X_m\\}$ of finite sets in $\\mathbb{R}^d$, we give conditions under which it is possible to chose a point $x_i\\in X_i$, in such a way that the points $\\{x_1,...,x_m\\}\\subset \\mathbb{R}^d$ are in general position. The proof uses topological techniques in the spirit of Aharoni and Haxell's celebrated generalization of Hall's theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-20T10:40:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "geometric hall-type theorem",
      "halls marriage theorem",
      "halls theorem",
      "haxells celebrated generalization",
      "general position"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.6639H"
    }
  }
}