Singular combinatorics

Details Singular combinatorics Singular combinatorics

2003-04-28

arxiv.org/abs/math/0304465v1

Proceedings of the ICM, Beijing 2002, vol. 3, 561--572

Mathematics

Combinatorics

Scientific paper

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.

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