标题： 图因子的渐近计数通过累积量展开 显示英文标题

标题： Asymptotic enumeration of graph factors by cumulant expansion

摘要： 令$G$为一个具有良好扩展性质且不太接近二分图的稠密图。 令$\boldsymbol d$为一个图度序列。 在非常弱的条件下，我们可以以任意精度找到$G$中具有度序列$\boldsymbol d$的子图数量。 平均度可以是$n$的任何幂，度的变化可以非常大。 该方法使用了第一作者找到的累积生成函数尾部的显式界。 作为第一个应用，我们证明了正则图数量存在渐近展开式，并显式地找到了几个项。 我们认为这是首次在组合应用中使用傅里叶反演方法，其中主导区域之外的积分无法通过绝对值积分来界定，我们给出了处理这种情况的一般方法。 显示英文摘要

摘要： Let $G$ be a dense graph with good expansion properties and not too close to being bipartite. Let $\boldsymbol d$ be a graphical degree sequence. Under very weak conditions, we find the number of subgraphs of $G$ with degree sequence $\boldsymbol d$ to arbitrary precision. The average degree can be any power of $n$ and the variation in degrees can be very large. The method uses an explicit bound on the tail of the cumulant generating function found by the first author. As a first application, we prove that there is an asymptotic expansion for the number of regular graphs and find several terms explicitly. We believe that this is the first combinatorial application of the Fourier inversion method for which the integral outside the dominant regions cannot be bounded by the integral of the absolute value, and we give a general method for dealing with that situation.