{
  "id": "1607.03600",
  "version": "v1",
  "published": "2016-07-13T06:24:07.000Z",
  "updated": "2016-07-13T06:24:07.000Z",
  "title": "The Elekes-Szabó Theorem in four dimensions",
  "authors": [
    "Orit E. Raz",
    "Micha Sharir",
    "Frank de Zeeuw"
  ],
  "comment": "15 pages. arXiv admin note: text overlap with arXiv:1504.05012",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "Let $F\\in\\mathbb{C}[x,y,s,t]$ be an irreducible constant-degree polynomial, and let $A,B,C,D\\subset\\mathbb{C}$ be finite sets of size $n$. We show that $F$ vanishes on at most $O(n^{8/3})$ points of the Cartesian product $A\\times B\\times C\\times D$, unless $F$ has a special group-related form. A similar statement holds for $A,B,C,D$ of unequal sizes. This is a four-dimensional extension of our recent improved analysis of the original Elekes-Szab\\'o theorem in three dimensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-13T06:24:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dimensions",
      "original elekes-szabo theorem",
      "similar statement holds",
      "four-dimensional extension",
      "unequal sizes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}