{
  "id": "2007.03984",
  "version": "v1",
  "published": "2020-07-08T09:40:54.000Z",
  "updated": "2020-07-08T09:40:54.000Z",
  "title": "Asymptotics of the number of 2-threshold functions",
  "authors": [
    "Elena Zamaraeva",
    "Jovisa Zunic"
  ],
  "comment": "25 pages",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "A $k$-threshold function over a two-dimensional rectangular grid $\\mathcal{G}_{m,n} = \\{0,\\dots,m-1\\} \\times \\{0,\\dots,n-1\\}$ is the conjunction of $k$ linear threshold functions over the same domain. In this paper we focus on the case $k=2$ and show that the number of 2-threshold functions defined on $\\mathcal{G}_{m,n}$ is $\\dfrac{25}{12\\pi^4} m^4 n^4 + o(m^4n^4)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-08T09:40:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03B50",
      "05A18",
      "52C05",
      "11P21",
      "G.2.1"
    ],
    "keywords": [
      "asymptotics",
      "linear threshold functions",
      "two-dimensional rectangular grid",
      "conjunction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}