Singular combinatorics
Combinatorics
2007-05-23 v1
Abstract
Combinatorial enumeration leads to counting generating functions presenting a wide variety of analytic types. Properties of generating functions at singularities encode valuable information regarding asymptotic counting and limit probability distributions present in large random structures. ``Singularity analysis'' reviewed here provides constructive estimates that are applicable in several areas of combinatorics. It constitutes a complex-analytic Tauberian procedure by which combinatorial constructions and asymptotic--probabilistic laws can be systematically related.
Cite
@article{arxiv.math/0304465,
title = {Singular combinatorics},
author = {Philippe Flajolet},
journal= {arXiv preprint arXiv:math/0304465},
year = {2007}
}