{
  "id": "1706.03987",
  "version": "v1",
  "published": "2017-06-13T10:28:16.000Z",
  "updated": "2017-06-13T10:28:16.000Z",
  "title": "Minimum supports of eigenfunctions of Johnson graphs",
  "authors": [
    "Konstantin Vorob'ev",
    "Ivan Mogilnykh",
    "Alexandr Valyuzhenich"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We study the weights of eigenvectors of the Johnson graphs $J(n,w)$. For any $i \\in \\{1,\\ldots,w\\}$ and sufficiently large $n, n\\geq n(i,w)$ we show that an eigenvector of $J(n,w)$ with the eigenvalue $\\lambda_i=(n-w-i)(w-i)-i$ has at least $2^i(^{n-2i}_{w-i})$ nonzeros and obtain a characterization of eigenvectors that attain the bound.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-13T10:28:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "johnson graphs",
      "minimum supports",
      "eigenfunctions",
      "eigenvector"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}