{
  "id": "1807.09201",
  "version": "v1",
  "published": "2018-07-18T09:27:25.000Z",
  "updated": "2018-07-18T09:27:25.000Z",
  "title": "Every square can be tiled with T-tetrominos and no more than 5 monominos",
  "authors": [
    "Jack Grahl"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "If n is a multiple of 4, then a square of side n can be tiled with T-tetrominos, using a well-known construction. If n is even but not a multiple of four, then there exists an equally well-known construction for tiling a square of side n with T-tetrominos and exactly 4 monominos. On the other hand, it was shown by Walkup that it is not possible to tile the square using only T-tetrominos. Now consider the remaining cases, where n is odd. It was shown by Zhan that it is not possible to tile such a square using only one monomino. Hochberg showed that no more than 9 monominos are ever needed. We give a construction for all odd n which uses exactly 5 monominos, thereby resolving this question.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-18T09:27:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "t-tetrominos",
      "equally well-known construction",
      "remaining cases"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}