| Analytic Combinatorics of Non-crossing Configurations (2007) | |||||||||||||
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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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