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Singular Combinatorics (2002)
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| Venue: | ICM 2002 VOL. III 1-3 |
| Citations: | 796 - 10 self |
BibTeX
@MISC{Flajolet02singularcombinatorics,
author = {Philippe Flajolet},
title = {Singular Combinatorics },
year = {2002}
}
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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.
Keyphrases
singular combinatorics combinatorial construction complex-analytic tauberian procedure asymptotic counting constructive estimate wide variety combinatorial enumeration valuable information analytic type asymptotic-probabilistic law several area limit probability distribution singularity analysis large random structure
