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Twenty Combinatorial Examples of Asymptotics Derived from Multivariate Generating Functions
2008
SIAM Review
Let {ar : r ∈ N d } be a d-dimensional array of numbers for which the generating function F (z) := r arz r is meromorphic in a neighborhood of the origin. For example, F may be a rational multivariate generating function. We discuss recent results that allow the effective computation of asymptotic expansions for the coefficients of F . Our purpose is to illustrate the use of these techniques on a variety of problems of combinatorial interest. The survey begins by summarizing previous work on
doi:10.1137/050643866
fatcat:xzp7nflc5ze3vaa2ryzbf5hi2u