论文标题
双曲动物的等法公式
Isoperimetric Formulas for Hyperbolic Animals
论文作者
论文摘要
动物是一种平面形状，通过将一致的常规多边形沿其边缘连接起来形成。 1976年，Harary和Harbourth为欧几里得动物提供了封闭的等速度公式。在这里，我们为双曲动物提供类似的公式。我们通过证明斯特里式单词与图形中由双曲线镶嵌确定的球中的离散类似物的参数之间的联系来做到这一点。这揭示了双曲动物的复杂性，而欧几里得动物不存在。
An animal is a planar shape formed by attaching congruent regular polygons along their edges. In 1976, Harary and Harborth gave closed isoperimetric formulas for Euclidean animals. Here, we provide analogous formulas for hyperbolic animals. We do this by proving a connection between Sturmian words and the parameters of a discrete analogue of balls in the graph determined by hyperbolic tessellations. This reveals a complexity in hyperbolic animals that is not present in Euclidean animals.
