Multivariate Asymptotics for Products of Large Powers with Applications to Lagrange Inversion

An asymptotic estimate is given for the coefficients of products of large powers of generating functions. This theorem and another local limit theorem which is useful for conditioning are applied to various combinatorial enumeration problems that involve multivariate Lagrange inversion. 1991 AMS Class. No. Primary: 41A63 Secondary: 05A16, 05C05, 41A60 

• Type: Journal
• Year: 1999
• Where: COMBINATORICS
• Authors: Edward A. Bender, L. Bruce Richmond
• Keywords: Asymptotic Estimate, Combinatorial Enumeration Problems, COMBINATORICS 1999, Multivariate Lagrange Inversion