Singularity analysis, Hadamard products, and tree recurrences

Details Singularity analysis, Hadamard products, and tree recurrences Singularity analysis, Hadamard products, and tree recurrences

2003-06-13

arxiv.org/abs/math/0306225v1

J. Comput. Appl. Math. 174 (2005) 271-313

Mathematics

Combinatorics

47 pages. Submitted for publication

Scientific paper

10.1016/j.cam.2004.04.014

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

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