拉丁多面体
Latin Polytopes
摘要：
拉丁方是研究得很好的组合对象。在本文中，我们推广的概念，并提出新的对象，如拉丁三角形，自由拉丁方，拉丁四面体，自由拉丁立方体等，我们开始与一个经典的定义拉丁方其次是一个基于拉丁化板的概念。于是，一个拉丁方就表现为一种组合设计，它的点是几何的，而它的线（行和列）在正方形的对称性下是不变的。下面的概括继续进行1。拓宽了这种几何对称性2.考虑点的更一般的配置，以及3.允许更自由地相交的线。由此产生的概念是拉丁董事会。最后，我们将拉丁板特殊化，定义了拉丁多面体、拉丁多边形和拉丁多面体。
英文摘要：
Latin squares are well studied combinatorial objects. In this paper we generalize the concept and propose new objects like Latin triangles, free Latin squares, Latin tetrahedra, free Latin cubes, etc. We start with a classic definition of Latin squares followed by one based on the concept of latinized board. A Latin square appears then as a combinatorial design whose points are geometric and whose lines (the rows and columns) are invariant under the symmetries of the square. The generalization that follows proceeds by 1. broadening this geometric symmetry 2. considering more general configurations of points and 3. admitting lines that intersect more freely. The resulting concept is the Latin board. Finally, we particularize Latin boards to define Latin polytopes, Latin polygons and Latin polyhedra.
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