{
  "id": "1805.03778",
  "version": "v1",
  "published": "2018-05-10T01:40:23.000Z",
  "updated": "2018-05-10T01:40:23.000Z",
  "title": "Threshold functions for patterns in random subsets of finite vector spaces",
  "authors": [
    "Changhao Chen",
    "Catherine Greenhill"
  ],
  "comment": "15 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We study the existence of certain \"patterns\" in random subsets of vector spaces over finite fields. The patterns we consider are three-term arithmetic progressions, right triangles, parallelograms and affine planes. We give a threshold function for the property that a random subset of vectors contains a pattern from a given family, and show that the number of patterns contained in the random subset is asymptotically Poisson at the threshold scale.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-10T01:40:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random subset",
      "finite vector spaces",
      "threshold function",
      "three-term arithmetic progressions",
      "right triangles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}