{
  "id": "1505.03697",
  "version": "v1",
  "published": "2015-05-14T12:00:44.000Z",
  "updated": "2015-05-14T12:00:44.000Z",
  "title": "Tiling with arbitrary tiles",
  "authors": [
    "Vytautas Gruslys",
    "Imre Leader",
    "Ta Sheng Tan"
  ],
  "comment": "23 pages, 19 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $T$ be a tile in $\\mathbb{Z}^n$, meaning a finite subset of $\\mathbb{Z}^n$. It may or may not tile $\\mathbb{Z}^n$, in the sense of $\\mathbb{Z}^n$ having a partition into copies of $T$. However, we prove that $T$ does tile $\\mathbb{Z}^d$ for some $d$. This resolves a conjecture of Chalcraft.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-14T12:00:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B45",
      "05B50",
      "52C22"
    ],
    "keywords": [
      "arbitrary tiles",
      "finite subset",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}