{
  "id": "2103.11198",
  "version": "v1",
  "published": "2021-03-20T15:46:49.000Z",
  "updated": "2021-03-20T15:46:49.000Z",
  "title": "Note on the number of balanced independent sets in the Hamming cube",
  "authors": [
    "Jinyoung Park"
  ],
  "comment": "6 pages. Comments are welcome!",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $Q_d$ be the $d$-dimensional Hamming cube and $N=|V(Q_d)|=2^d$. An independent set $I$ in $Q_d$ is called balanced if $I$ contains the same number of even and odd vertices. We show that the logarithm of the number of balanced independent sets in $Q_d$ is \\[(1-\\Theta(1/\\sqrt d))N/2.\\] The key ingredient of the proof is an improved version of \"Sapozhenko's graph container lemma.\"",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-20T15:46:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "balanced independent sets",
      "sapozhenkos graph container lemma",
      "odd vertices",
      "dimensional hamming cube"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}