论文标题
从方向链组成的树型图的枚举
Enumeration of tree-type diagrams assembled from oriented chains of edges
论文作者
论文摘要
我们研究了离散ERD ERD \ H OS-Rényi随机矩阵模型中累积扩张的研究中出现的树型图。使用Pr \“ UFER代码的版本，我们获得了从$ k $ $ q $ edges组装的树类图的数量的明确表达式。使用此修改后的Prüfer编纂，我们获得了超级加权树型的明确表达式，这些表达式是根据Edge的多重范围来汇总的。 常规的。
We study a family of tree-type diagrams that arise in studies of the cumulant expansion in discrete Erd\H os-Rényi random matrix models. Using a version of the Pr\" ufer code, we obtain an explicit expression for the number of tree-type diagrams assembled from $k$ oriented chains of $q$ edges. Using this modified Prüfer codification, we get an explicit expression for sum overs weighted tree-type diagrams with a weight depending on multiplicity of edges. We describe similar results for tree-type diagrams assembled from chains that are not necessarily regular.
