Papers › T-Tetrominos in Arithmetic Progression
T-Tetrominos in Arithmetic Progression
Emily Feller, Robert Hochberg
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A famous result of D. Walkup is that an m×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 4×4 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.
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