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.
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https://hal.inria.fr/inria-00073493
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Submitted on : Wednesday, May 24, 2006 - 1:02:32 PM
Last modification on : Friday, May 25, 2018 - 12:02:02 PM
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  • HAL Id : inria-00073493, version 1

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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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