{
  "id": "1912.08181",
  "version": "v1",
  "published": "2019-12-17T18:41:11.000Z",
  "updated": "2019-12-17T18:41:11.000Z",
  "title": "A remark on sets with few distances in $\\mathbb{R}^{d}$",
  "authors": [
    "Fedor Petrov",
    "Cosmin Pohoata"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A celebrated theorem due to Bannai-Bannai-Stanton says that if $A$ is a set of points in $\\mathbb{R}^{d}$, which determines $s$ distinct distances, then $$|A| \\leq {d+s \\choose s}.$$ In this note, we give a new simple proof of this result by combining Sylvester's Law of Inertia for quadratic forms with the proof of the so-called Croot-Lev-Pach Lemma from additive combinatorics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-17T18:41:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quadratic forms",
      "bannai-bannai-stanton says",
      "combining sylvesters law",
      "croot-lev-pach lemma",
      "simple proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}