{
  "id": "1602.05738",
  "version": "v1",
  "published": "2016-02-18T10:07:55.000Z",
  "updated": "2016-02-18T10:07:55.000Z",
  "title": "Periodicity and decidability of tilings of $\\mathbb{Z}^{2}$",
  "authors": [
    "Siddhartha Bhattacharya"
  ],
  "categories": [
    "math.CO",
    "math.DS"
  ],
  "abstract": "We prove that any finite set $F\\subset {\\mathbb{Z}^2}$ that tiles ${\\mathbb{Z}^2}$ by translations also admits a periodic tiling. As a consequence, the problem whether a given finite set $F$ tiles ${\\mathbb{Z}^2}$ is decidable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-18T10:07:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52C20",
      "37A15"
    ],
    "keywords": [
      "periodicity",
      "finite set",
      "decidability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160205738B"
    }
  }
}