论文标题
关于Haros图的程度分布
On the degree distribution of Haros graphs
论文作者
论文摘要
HAROS图是单位间隔中实数的图理论表示。 HAROS图的度分布提供了有关拓扑结构和相关实际数字的信息。本文提供了有关程度分布的分析公式的猜想的全面证明。具体而言，定理概述了Haros图，其相关实际数字的相应持续部分以及Farey二进制树中随后的符号路径之间的关系。此外，在Farey部分定义的子间隔中的表达连续和细分线性可以从Haros图的度分布的附加结论中得出。
Haros graphs is a graph-theoretical representation of real numbers in the unit interval. The degree distribution of the Haros graphs provides information regarding the topological structure and the associated real number. This article provides a comprehensive demonstration of a conjecture concerning the analytical formulation of the degree distribution. Specifically, a theorem outlines the relationship between Haros graphs, the corresponding continued fraction of its associated real number, and the subsequent symbolic paths in the Farey binary Tree. Moreover, an expression continuous and piece-wise linear in subintervals defined by Farey fractions can be derived from an additional conclusion for the degree distribution of Haros graphs.
