{
  "id": "2006.02877",
  "version": "v1",
  "published": "2020-06-04T14:19:54.000Z",
  "updated": "2020-06-04T14:19:54.000Z",
  "title": "A subexponential upper bound for van der Waerden numbers W(3,k)",
  "authors": [
    "Tomasz Schoen"
  ],
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "We show an improved upper estimate for van der Waerden number $W(3,k):$ there is an absolute constant $c>0$ such that if $\\{1,\\dots,N\\}=X\\cup Y$ is a partition such that $X$ does not contain any arithmetic progression of length $3$ and $Y$ does not contain any arithmetic progression of length $k$ then $$N\\le \\exp(O(k^{1-c}))\\,.$$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-04T14:19:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D10",
      "11B25"
    ],
    "keywords": [
      "van der waerden number",
      "subexponential upper bound",
      "arithmetic progression",
      "absolute constant",
      "upper estimate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}