A famous result of D. Walkup is that an rectangle may be tiled by T-tetrominos if and only if both and are multiples of 4. The “if” portion may be proved by tiling a 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.

中文翻译：

---

算术级数中的 T-四格骨牌

D. Walkup 的一个著名结果是，当且仅当 和 都是 4 的倍数时，矩形才可以被 T-tetrominos 平铺。“if”部分可以通过平铺一个块，然后复制该块来填充长方形;但这会导致定期的、周期性的平铺。在本文中，我们研究了 T-tetrominos 矩形的每个平铺中必须存在多少“顺序”，其中我们通过平铺的算术级数的长度来测量顺序。