带多米诺骨牌的矩形、三角形、圆环形和默比乌斯带的无故障可铺性
Fault-Free Tileability of Rectangles, Cylinders, Tori, and Möbius Strips with Dominoes
摘要：
我们周围到处都是瓦片，我们的好奇心吸引我们去研究它们的特性。瓷砖是一种在木板上排列棋子的方式，这样就没有未覆盖的空间，也没有被一个以上瓷砖覆盖的空间。特别是，我们研究了无故障平铺板与多米诺骨牌。为了无故障，与瓷砖相交的每条线也必须与至少一个瓷砖的内部相交。无故障矩形板已经得到了很好的研究，但我们看看板是圆柱体，环面，和默比乌斯带。使用多米诺骨牌，我们研究各种形状的董事会，看看如何瓷砖的变化。我们得到了圆柱、圆环和默比乌斯带的完整结果。
英文摘要：
Tilings are around us everywhere, and our curiosity draws us to study their properties. A tiling is a way of arranging pieces on a board, such that there is no space left uncovered, nor any space covered by more than one tile. In particular, we study fault-free tilings of boards with dominoes. To be fault-free every line that intersects the tiling must also intersect the interior of at least one of the tiles. Fault-free rectangular boards have been well studied, however we look at boards that are cylinders, tori, and Möbius strips. Using dominoes we study the various shapes of boards and see how the tileability changes. We have complete results for cylinders, tori, and Möbius strips.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
