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Reports (Research Report) Year : 1997

## Analytic Combinatorics of Non-crossing Configurations

(1) ,
1
Philippe Flajolet
• Function : Author
• PersonId : 829512
Marc Noy
• Function : Author

#### 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.

#### Domains

Computer Science [cs] Other [cs.OH]

### Dates and versions

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

### Identifiers

• HAL Id : inria-00073493 , version 1

### Cite

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

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