HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Conference papers

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.
Complete list of metadata

Cited literature [16 references]  Display  Hide  Download

https://hal.inria.fr/hal-02353375
Contributor : Vincent Pilaud Connect in order to contact the contributor
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

Collections

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⟩

Share

Metrics

Record views

10

Files downloads

35