Asymptotics of bivariate analytic functions with algebraic singularities

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:153

Article

Greenwood, Torin¹ 

[1] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

关键词: Generating functions;    Coefficients;    Asymptotics;    Multivariate;    Singularity analysis;    Algebraic;   

DOI  :  10.1016/j.jcta.2017.06.014

来源: Elsevier

【 摘 要 】

In this paper, we use the multivariate analytic techniques of Pemantle and Wilson to derive asymptotic formulae for the coefficients of a broad class of multivariate generating functions with algebraic singularities. Then, we apply these results to a generating function encoding information about the stationary distributions of a graph coloring algorithm studied by Butler, Chung, Cummings, and Graham (2015). Historically, Flajolet and Odlyzko (1990) analyzed the coefficients of a class of univariate generating functions with algebraic singularities. These results have been extended to classes of multivariate generating functions by Gao and Richmond (1992) and Hwang (1996, 1998), in both cases by immediately reducing the multivariate case to the univariate case. Pemantle and Wilson (2013) outlined new multivariate analytic techniques and used them to analyze the coefficients of rational generating functions. These multivariate techniques are used here to analyze functions with algebraic singularities. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free