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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.
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Dates and versions

hal-02353375 , version 1 (07-11-2019)

Identifiers

  • HAL Id : hal-02353375 , version 1

Cite

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⟩
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