# Analytic combinatorics of chord and hyperchord diagrams with $k$ crossings

Abstract : Using methods from Analytic Combinatorics, we study the families of perfect matchings, partitions, chord diagrams, and hyperchord diagrams on a disk with a prescribed number of crossings. For each family, we express the generating function of the configurations with exactly $k$ crossings as a rational function of the generating function of crossing-free configurations. Using these expressions, we study the singular behavior of these generating functions and derive asymptotic results on the counting sequences of the configurations with precisely $k$ crossings. Limiting distributions and random generators are also studied.
Keywords :
Document type :
Conference papers
Domain :

Cited literature [16 references]

https://hal.inria.fr/hal-02353375
Contributor : Vincent Pilaud <>
Submitted on : Thursday, November 7, 2019 - 11:54:09 AM
Last modification on : Monday, November 16, 2020 - 3:56:03 PM
Long-term archiving on: : Saturday, February 8, 2020 - 9:48:39 PM

### File

PilaudRue_QuasiPlanarFamilies_...
Files produced by the author(s)

### Identifiers

• HAL Id : hal-02353375, version 1

### Citation

Vincent Pilaud, Juanjo Rué. Analytic combinatorics of chord and hyperchord diagrams with $k$ crossings. 25th International Meeting on Probabilistic, Combinatorial, and Asymptotic Methods in the Analysis of Algorithms (AofA'14), Jun 2014, Paris, France. pp.339-350. ⟨hal-02353375⟩

Record views