{
  "id": "math/0503367",
  "version": "v2",
  "published": "2005-03-17T18:29:18.000Z",
  "updated": "2005-04-05T19:27:34.000Z",
  "title": "Sets of k-recurrence but not (k+1)-recurrence",
  "authors": [
    "N. Frantzikinakis",
    "E. Lesigne",
    "M. Wierdl"
  ],
  "comment": "8 pages",
  "categories": [
    "math.DS",
    "math.CO"
  ],
  "abstract": "For every $k\\in \\mathbb{N}$, we produce a set of integers which is $k$-recurrent but not $(k+1)$-recurrent. This extends a result of Furstenberg who produced a 1-recurrent set which is not 2-recurrent. We discuss a similar result for convergence of multiple ergodic averages. Finally, we also point out a combinatorial consequence related to Szemer\\' edi's theorem.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-04-05T19:27:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A45",
      "28D05"
    ],
    "keywords": [
      "k-recurrence",
      "multiple ergodic averages",
      "edis theorem",
      "similar result",
      "furstenberg"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......3367F"
    }
  }
}