{
  "id": "2003.13598",
  "version": "v1",
  "published": "2020-03-30T16:29:01.000Z",
  "updated": "2020-03-30T16:29:01.000Z",
  "title": "Weakly norming graphs are edge-transitive",
  "authors": [
    "Alexander Sidorenko"
  ],
  "comment": "4 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $\\mathcal{H}$ be the class of bounded measurable symmetric functions on $[0,1]^2$. For a function $h \\in \\mathcal{H}$ and a graph $G$ with vertex set $\\{v_1,\\ldots,v_n\\}$ and edge set $E(G)$, define \\[ t_G(h) \\; = \\; \\int \\cdots \\int \\prod_{\\{v_i,v_j\\} \\in E(G)} h(x_i,x_j) \\: dx_1 \\cdots dx_n \\: . \\] We prove that if $t_G(|h|)^{1/|E(G)|}$ is a norm on $\\mathcal{H}$, then $G$ is edge-transitive.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-30T16:29:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "weakly norming graphs",
      "edge-transitive",
      "edge set",
      "vertex set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}