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Analytic combinatorics in 𝑑 variables: an overview
[unknown]
2010
Contemporary Mathematics
unpublished
Preserved Fulltext
Let F (Z) = P r arZ r be a rational generating function in the d variables Z 1 , . . . , Z d . Asymptotic formulae for the coefficients ar may be obtained via Cauchy's integral formula in C d . Evaluation of this integral is not as straightforward as it is in the univariate case. This paper discusses geometric techniques that are needed for evaluation of these integrals and surveys classes of functions for which these techniques lead to explicit and effectively computable asymptotic formulae.
doi:10.1090/conm/520/10260
fatcat:tvxn4l4tdzg73omd3srpxidkwq