2003/06/13 by James Allen Fill, Philippe Flajolet, Nevin Kapur
Mathematics · #math.CO #math.PR #msc:05A16 #msc:40E99 #msc:68W40
paper · pdf · doi:10.1016/j.cam.2004.04.014
published as J. Comput. Appl. Math. 174 (2005) 271-313 · 47 pages. Submitted for publication
arxiv created 2003/06/13 · arxiv updated 2009/11/30
We present a toolbox for extracting asymptotic information on the coefficients of combinatorial generating functions. This toolbox notably includes a treatment of the effect of Hadamard products on singularities in the context of the complex Tauberian technique known as singularity analysis. As a consequence, it becomes possible to unify the analysis of a number of divide-and-conquer algorithms, or equivalently random tree models, including several classical methods for sorting, searching, and dynamically managing equivalence relations