{
  "id": "2004.03060",
  "version": "v1",
  "published": "2020-04-07T01:04:54.000Z",
  "updated": "2020-04-07T01:04:54.000Z",
  "title": "Independent sets in middle two layers of Boolean lattice",
  "authors": [
    "József Balogh",
    "Ramon I. Garcia",
    "Lina Li"
  ],
  "comment": "19 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "For an odd integer $n=2d-1$, let $\\mathcal{B}(n, d)$ be the subgraph of the hypercube $Q_n$ induced by the two largest layers. In this paper, we describe the typical structure of independent sets in $\\mathcal{B}(n, d)$ and give precise asymptotics on the number of them. The proofs use Sapozhenko's graph container method and a recently developed method of Jenssen and Perkins, which combines Sapozhenko's graph container lemma with the cluster expansion for polymer models from statistical physics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-07T01:04:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "independent sets",
      "boolean lattice",
      "sapozhenkos graph container lemma",
      "sapozhenkos graph container method",
      "largest layers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}