论文标题
算术进展中的T-四氨基
T-Tetrominos in Arithmetic Progression
论文作者
论文摘要
D. Walkup的一个著名结果是，当$ m \ times n $矩形可以被t-tetrominos铺上时，并且只有当$ m $和$ n $都是4的倍数。但是，这导致了定期的，周期性的瓷砖。在本文中，我们研究了t-tetrominios的矩形每个瓷砖中必须存在多少“顺序”，在那里我们根据瓷砖的算术渐进式测量顺序。
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.
