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Analytic combinatorics of chord and hyperchord diagrams with k crossings

Author
Pilaud, V.; Rue, J.
Type of activity
Journal article
Journal
Advances in applied mathematics
Date of publication
2014-05-07
Volume
57
First page
60
Last page
100
DOI
https://doi.org/10.1016/j.aam.2014.04.001 Open in new window
Repository
http://hdl.handle.net/2117/85728 Open in new window
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 countin...
Citation
Pilaud, V., Rue, J. Analytic combinatorics of chord and hyperchord diagrams with k crossings. "Advances in applied mathematics", 07 Maig 2014, vol. 57, p. 60-100.
Keywords
analytic combinatorics, chord diagrams, generating functions, quasi-planar configurations
Group of research
GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics

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