Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4624715 | Advances in Applied Mathematics | 2014 | 41 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Vincent Pilaud, Juanjo Rué,