{
  "id": "1706.08118",
  "version": "v1",
  "published": "2017-06-25T15:10:10.000Z",
  "updated": "2017-06-25T15:10:10.000Z",
  "title": "Large sets avoiding linear patterns",
  "authors": [
    "Alexia Yavicoli"
  ],
  "comment": "9 pages",
  "categories": [
    "math.CA",
    "math.CO",
    "math.MG"
  ],
  "abstract": "We prove that for any dimension function $h$ with $h \\prec x^d$ and for any countable set of linear patterns, there exists a compact set $E$ with $\\mathcal{H}^h(E)>0$ avoiding all the given patterns. We also give several applications and recover results of Keleti, Maga, and Mathe.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-25T15:10:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A78"
    ],
    "keywords": [
      "large sets avoiding linear patterns",
      "compact set",
      "dimension function",
      "countable set",
      "applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}