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COMBINATORICS
2006

A Hybrid of Darboux's Method and Singularity Analysis in Combinatorial Asymptotics

9 years 2 months ago
A Hybrid of Darboux's Method and Singularity Analysis in Combinatorial Asymptotics
A "hybrid method", dedicated to asymptotic coefficient extraction in combinatorial generating functions, is presented, which combines Darboux's method and singularity analysis theory. This hybrid method applies to functions that remain of moderate growth near the unit circle and satisfy suitable smoothness assumptions--this, even in the case when the unit circle is a natural boundary. A prime application is to coefficients of several types of infinite product generating functions, for which full asymptotic expansions (involving periodic fluctuations at higher orders) can be derived. Examples relative to permutations, trees, and polynomials over finite fields are treated in this way.
Philippe Flajolet, Éric Fusy, Xavier Gourdo
Added 11 Dec 2010
Updated 11 Dec 2010
Type Journal
Year 2006
Where COMBINATORICS
Authors Philippe Flajolet, Éric Fusy, Xavier Gourdon, Daniel Panario, Nicolas Pouyanne
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