论文标题
多元序列IV的渐近学：用极平面布置的极点生成函数
Asymptotics of multivariate sequences IV: generating functions with poles on a hyperplane arrangement
论文作者
论文摘要
令F为线性函数的产物分析函数的商。在几个变量的分析组合框架中工作，我们使用多变量残基和鞍点近似来计算F的泰勒系数的渐近公式。因为奇异的F是超平面的结合，所以我们能够显式使在多元奇异性分析中出现的拓扑分解。除了有效和明确的渐近结果外，我们还为不同的渐近方案之间的过渡提供了第一个结果，并提供了第一个软件包，以在几个变量中的非平滑分析组合案例中验证和计算渐近性。我们也希望本文将作为组合主义者的几个变量中更先进的分析组合学的角落。
Let F be the quotient of an analytic function with a product of linear functions. Working in the framework of analytic combinatorics in several variables, we compute asymptotic formulae for the Taylor coefficients of F using multivariate residues and saddle-point approximations. Because the singular set of F is the union of hyperplanes, we are able to make explicit the topological decompositions which arise in the multivariate singularity analysis. In addition to effective and explicit asymptotic results, we provide the first results on transitions between different asymptotic regimes, and provide the first software package to verify and compute asymptotics in non-smooth cases of analytic combinatorics in several variables. It is also our hope that this paper will serve as an entry to the more advanced corners of analytic combinatorics in several variables for combinatorialists.
