{
  "id": "1901.00440",
  "version": "v1",
  "published": "2018-12-20T15:18:33.000Z",
  "updated": "2018-12-20T15:18:33.000Z",
  "title": "On a question of Sidorenko",
  "authors": [
    "D. Cherkashin",
    "F. Petrov",
    "V. Sokolov"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "For a positive integer $n>1$ denote by $\\omega(n)$ the maximal possible number $k$ of different functions $f_1,\\dots,f_k:\\mathbb{Z}/n\\mathbb{Z}\\mapsto \\mathbb{Z}/n\\mathbb{Z}$ such that each function $f_i-f_j,i<j$, is bijective. Recently A. Sidorenko conjectured that $\\omega(n)$ equals to the minimal prime divisor of $n$. We disprove it for $n=15,21,27$ by several counterexamples found by computer.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-20T15:18:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "minimal prime divisor",
      "positive integer",
      "counterexamples"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}