{
  "id": "2102.08995",
  "version": "v1",
  "published": "2021-02-17T19:39:15.000Z",
  "updated": "2021-02-17T19:39:15.000Z",
  "title": "Integer colorings with no rainbow 3-term arithmetic progression",
  "authors": [
    "Xihe Li",
    "Hajo Broersma",
    "Ligong Wang"
  ],
  "comment": "13 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we study the rainbow Erd\\H{o}s-Rothschild problem with respect to 3-term arithmetic progressions. We obtain the asymptotic number of $r$-colorings of $[n]$ without rainbow 3-term arithmetic progressions, and we show that the typical colorings with this property are 2-colorings. We also prove that $[n]$ attains the maximum number of rainbow 3-term arithmetic progression-free $r$-colorings among all subsets of $[n]$. Moreover, the exact number of rainbow 3-term arithmetic progression-free $r$-colorings of $\\mathbb{Z}_p$ is obtained, where $p$ is any prime and $\\mathbb{Z}_p$ is the cyclic group of order $p$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-17T19:39:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B25",
      "11B75",
      "05C55"
    ],
    "keywords": [
      "integer colorings",
      "arithmetic progression-free",
      "maximum number",
      "asymptotic number",
      "exact number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}