Analytic Combinatorics of Non-crossing Configurations

Philippe Flajolet 1 Marc Noy
1 ALGO - Algorithms
Inria Paris-Rocquencourt
Abstract : 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.
Type de document :
Rapport
[Research Report] RR-3196, INRIA. 1997
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https://hal.inria.fr/inria-00073493
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Soumis le : mercredi 24 mai 2006 - 13:02:32
Dernière modification le : mardi 17 avril 2018 - 11:25:21
Document(s) archivé(s) le : jeudi 24 mars 2011 - 12:51:21

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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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