{
  "id": "1604.00842",
  "version": "v1",
  "published": "2016-04-04T13:01:23.000Z",
  "updated": "2016-04-04T13:01:23.000Z",
  "title": "Homological connectivity of random hypergraphs",
  "authors": [
    "Oliver Cooley",
    "Penny Haxell",
    "Mihyun Kang",
    "Philipp Sprüssel"
  ],
  "comment": "21 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We consider simplicial complexes that are generated from the binomial random 3-uniform hypergraph by taking the downward-closure. We determine when this simplicial complex is homologically connected, meaning that its zero-th and first homology groups with coefficients in $\\mathbb{F}_2$ vanish. Although this is not intrinsically a monotone property, we show that it nevertheless has a single sharp threshold, and indeed prove a hitting time result relating the connectedness to the disappearance of the last minimal obstruction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-04T13:01:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C80",
      "05C65",
      "05E45"
    ],
    "keywords": [
      "random hypergraphs",
      "homological connectivity",
      "simplicial complex",
      "first homology groups",
      "single sharp threshold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160400842C"
    }
  }
}