论文标题
Conway-Coxeter Frieze模式中的子病因
Subpolygons in Conway-Coxeter frieze patterns
论文作者
论文摘要
带有系数的架子是地图，将数字分配给常规多边形的边缘和对角线，以便满足所有用于越过对角线的托勒密关系。其中，经典的Conway-Coxeter Friezes是所有值均为自然数，所有边缘都有1的值。Conway-Coxeter Frieze的每个子分子都产生一个带有系数的frize。在本文中，我们提供了一个完整的算术标准，其系数的frizes似乎是Conway-Coxeter Friezes的子分子。这概括了我们早期与彼得·乔根森（Peter Jorgensen）从三角形到任意大小子分子的结果的结果。
Friezes with coefficients are maps assigning numbers to the edges and diagonals of a regular polygon such that all Ptolemy relations for crossing diagonals are satisfied. Among these, the classic Conway-Coxeter friezes are the ones where all values are natural numbers and all edges have value 1. Every subpolygon of a Conway-Coxeter frieze yields a frieze with coefficients over the natural numbers. In this paper we give a complete arithmetic criterion for which friezes with coefficients appear as subpolygons of Conway-Coxeter friezes. This generalizes a result of our earlier paper with Peter Jorgensen from triangles to subpolygons of arbitrary size.
