{
  "id": "2008.07757",
  "version": "v1",
  "published": "2020-08-18T06:16:34.000Z",
  "updated": "2020-08-18T06:16:34.000Z",
  "title": "Asymptotic enumeration of hypergraphs by degree sequence",
  "authors": [
    "Nina Kamčev",
    "Anita Liebenau",
    "Nick Wormald"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove an asymptotic formula for the number of $k$-uniform hypergraphs with a given degree sequence, for a wide range of parameters. In particular, we find a formula that is asymptotically equal to the number of $d$-regular $k$-uniform hypergraphs on $n$ vertices provided that $dn\\le c\\binom{n}{k}$ for a constant $c>0$, and $3 \\leq k < n^C$ for any $C<1/9.$ Our results relate the degree sequence of a random $k$-uniform hypergraph to a simple model of nearly independent binomial random variables, thus extending the recent results for graphs due to the second and third author.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-18T06:16:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A16",
      "05C30",
      "05C65"
    ],
    "keywords": [
      "degree sequence",
      "asymptotic enumeration",
      "uniform hypergraph",
      "independent binomial random variables",
      "asymptotic formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}