多元序列的渐近性，第III部分：二次点
Asymptotics of multivariate sequences, part III: quadratic points
摘要：
我们考虑了一些组合问题，其中有理生成函数可以得到，其分解子具有一定的奇异性的因素。具体地说，存在点附近的一个因素是渐近的一个非退化的二次。我们计算这样的生成函数的系数的渐近性。计算中需要对广义函数进行拓扑变形和傅里叶-拉普拉斯变换。我们将理论的结果应用于特定的组合问题，如阿兹特克钻石瓷砖，立方体小树林，和多集排列。
英文摘要：
We consider a number of combinatorial problems in which rational generating functions may be obtained, whose denominators have factors with certain singularities. Specifically, there exist points near which one of the factors is asymptotic to a nondegenerate quadratic. We compute the asymptotics of the coefficients of such a generating function. The computation requires some topological deformations as well as Fourier-Laplace transforms of generalized functions. We apply the results of the theory to specific combinatorial problems, such as Aztec diamond tilings, cube groves, and multi-set permutations.
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