Analytic combinatorics in š¯‘‘ variables: an overview
Robin Pemantle Ā· Contemporary mathematics - American Mathematical Society Ā· 2010
Let F(Z) = P r arZ r be a rational generating function in the d variables Z1, . . . , Zd. Asymptotic formulae for the coefficientsar 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.