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arXiv · 1307.6440

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

Vincent Pilaud·Juanjo Rué
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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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BibTeXRIS

Vincent Pilaud, Juanjo Rué. 2013-07-24. Analytic combinatorics of chord and hyperchord diagrams with $k$ crossings. https://doi.org/10.1016/j.aam.2014.04.001

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