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Reports (Research Report) Year : 1997

Analytic Combinatorics of Non-crossing Configurations

Philippe Flajolet
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Marc Noy
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This paper describes a systematic approach to the enumeration of «non-crossing» geometric configurations built on vertices of a convex $n$-gon in the plane. It relies on generating functions, symbolic methods, singularity analysis, and singularity perturbation. A consequence is exact and asymptotic counting results for trees, forests, graphs, connected graphs, dissections, and partitions. Limit laws of the Gaussian type are also established in this framework; they concern a variety of parameters like number of leaves in trees, number of components or edges in graphs, etc.


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inria-00073493 , version 1 (24-05-2006)


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Philippe Flajolet, Marc Noy. Analytic Combinatorics of Non-crossing Configurations. [Research Report] RR-3196, INRIA. 1997. ⟨inria-00073493⟩
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