{
  "id": "2203.12801",
  "version": "v1",
  "published": "2022-03-24T02:04:35.000Z",
  "updated": "2022-03-24T02:04:35.000Z",
  "title": "Threshold functions for incidence properties in finite vector spaces",
  "authors": [
    "Jeong Han Kim",
    "Ben Lund",
    "Thang Pham",
    "Semin Yoo"
  ],
  "comment": "17 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "The main purpose of this paper is to provide threshold functions for the events that a random subset of the points of a finite vector space has certain properties related to point-flat incidences. Specifically, we consider the events that there is an $\\ell$-rich $m$-flat with regard to a random set of points in $\\mathbb{F}_q^n$, the event that a random set of points is an $m$-blocking set, and the event that there is an incidence between a random set of points and a random set of $m$-flats. One of our key ingredients is a stronger version of a recent result obtained by Chen and Greenhill (2021).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-24T02:04:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite vector space",
      "threshold functions",
      "incidence properties",
      "random set",
      "main purpose"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}