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Diskr. Mat., 2004, Volume 16, Issue 2, Pages 121–135 (Mi dm158)  

This article is cited in 1 scientific paper (total in 1 paper)

Boundaries of a random triangulation of a disk

M. A. Krikun


Abstract: 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, grant 02–01–00415.

DOI: https://doi.org/10.4213/dm158

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English version:
Discrete Mathematics and Applications, 2004, 14:3, 301–315

Bibliographic databases:

UDC: 519.1
Received: 20.02.2003

Citation: 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
\Bibitem{Kri04}
\by M.~A.~Krikun
\paper Boundaries of a random triangulation of a disk
\jour Diskr. Mat.
\yr 2004
\vol 16
\issue 2
\pages 121--135
\mathnet{http://mi.mathnet.ru/dm158}
\crossref{https://doi.org/10.4213/dm158}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2084575}
\zmath{https://zbmath.org/?q=an:1121.60006}
\transl
\jour Discrete Math. Appl.
\yr 2004
\vol 14
\issue 3
\pages 301--315
\crossref{https://doi.org/10.1515/1569392031905548}


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  • https://doi.org/10.4213/dm158
  • http://mi.mathnet.ru/eng/dm/v16/i2/p121

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Krikun M., “Explicit enumeration of triangulations with multiple boundaries”, Electronic Journal of Combinatorics, 14:1 (2007), R61  mathscinet  zmath  isi
  • Дискретная математика
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