{
  "id": "2207.00533",
  "version": "v1",
  "published": "2022-07-01T16:33:10.000Z",
  "updated": "2022-07-01T16:33:10.000Z",
  "title": "T-Tetrominos in Arithmetic Progression",
  "authors": [
    "Emily Feller",
    "Robert Hochberg"
  ],
  "comment": "10 pages, 11 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "A famous result of D. Walkup is that an $m\\times n$ rectangle may be tiled by T-tetrominos if and only if both $m$ and $n$ are multiples of 4. The ``if'' portion may be proved by tiling a $4\\times 4$ block, and then copying that block to fill the rectangle; but, this leads to regular, periodic tilings. In this paper we investigate how much ``order'' must be present in every tiling of a rectangle by T-tetrominos, where we measure order by length of arithmetic progressions of tiles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-01T16:33:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D10",
      "05B45"
    ],
    "keywords": [
      "arithmetic progression",
      "t-tetrominos",
      "periodic tilings",
      "measure order",
      "famous result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}