This article is cited in 1 scientific paper (total in 1 paper)
Boundaries of a random triangulation of a disk
M. A. Krikun
We consider random triangulations of a disk with $k$ holes and $N$ triangles as $N\to\infty$. The coefficient $\lambda^m$, $\lambda>0$, is assigned to a triangulation with the total number of boundary edges equal to $m$. In the case of two boundaries, we separate three domains of variation of the parameter $\lambda$, and in each of them find the limit joint distribution of boundary lengths. For a greater number of boundaries, we give an algorithm to calculate the generating functions for the number of multi-rooted triangulations depending of the number of triangles and the lengths of boundaries. In Appendix, we discuss the relation between multi-rooted triangulations and unrooted triangulations, and give analogues of limit distributions for unrooted triangulations.
This research was supported by the Russian Foundation for Basic Research,
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Discrete Mathematics and Applications, 2004, 14:3, 301–315
M. A. Krikun, “Boundaries of a random triangulation of a disk”, Diskr. Mat., 16:2 (2004), 121–135; Discrete Math. Appl., 14:3 (2004), 301–315
Citation in format AMSBIB
\paper Boundaries of a random triangulation of a disk
\jour Diskr. Mat.
\jour Discrete Math. Appl.
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Krikun M., “Explicit enumeration of triangulations with multiple boundaries”, Electronic Journal of Combinatorics, 14:1 (2007), R61
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