2D Rubik's魔方的完整性
The Completeness of 2D Rubik's Shapes
摘要：
魔方是由Erno Rubik于1974年发明的，他不知道他的玩具会带来令人难以置信的流行和数学魅力。通过对立方体数学特性的多年研究，引入了魔方组来表示可以在立方体上执行的所有可能移动。在本文中，我们定义了一个平面类似的魔方，我们称之为魔方的广场，并证明了魔方的广场是完整的意义上说，任何两个配置有一个序列的移动，改变一个到另一个。魔方没有这个属性。然后，我们抽象的概念，魔方的广场，以魔方的形状和分析的完整性，在这个更一般的设置。
英文摘要：
The Rubik's cube was invented in 1974 by Erno Rubik, who had no idea of the incredible popularity and mathematical fascinations his toy would bring. Through the years of study on the mathematical properties of the cube, the Rubik's Cube group was introduced to represent all possible moves one could perform on the cube. In this paper, we define a planar analogue to the Rubik's cube, which we dub the Rubik's Square, and prove that the Rubik's square is complete in the sense that given any two configurations there is a sequence of moves which changes one to the other. The Rubik's cube does not have this property. We then abstract the concept of the Rubik's Square to a Rubik's Shape and analyse the completeness in this more general setting.
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