{
  "id": "2405.09322",
  "version": "v1",
  "published": "2024-05-15T13:22:42.000Z",
  "updated": "2024-05-15T13:22:42.000Z",
  "title": "The number of symmetric chain decompositions",
  "authors": [
    "István Tomon"
  ],
  "comment": "7 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove that the number of symmetric chain decompositions of the Boolean lattice $2^{[n]}$ is $$\\left(\\frac{n}{2e}+o(n)\\right)^{2^n}.$$ Furthermore, the number of symmetric chain decompositions of the hypergrid $[t]^n$ is $$n^{(1-o_n(1))\\cdot t^n}.$$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-15T13:22:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetric chain decompositions",
      "boolean lattice"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}