论文标题
具有给定的betti编号的连接的两分图的枚举
Enumeration of connected bipartite graphs with given Betti number
论文作者
论文摘要
我们获得了一阶线性偏微分方程，这些方程可通过为带有给定的betti编号的连接的两分图数量的两个变量的指数生成函数来满足。通过归纳求解这些方程，我们获得了产生函数的明确形式，并得出其系数的渐近行为。我们还介绍了一个基本图的家族，以对连接的两部分图进行分类，并将生成函数的另一种表达方式作为基本图的总和，这些函数的基本图是标有标记的双分子根生根树的数量。
We obtain first order linear partial differential equations which are satisfied by exponential generating functions of two variables for the number of connected bipartite graphs with given Betti number. By solving these equations inductively, we obtain the explicit form of generating functions and derive the asymptotic behavior of their coefficients. We also introduce a family of basic graphs to classify connected bipartite graphs and give another expression of the generating functions as the sum over basic graphs of rational functions of those for the number of labeled bipartite rooted spanning trees.
