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Enumerating simplicial decompositions of surfaces with boundaries

Author
Bernardi, O.; Rue, J.
Type of activity
Journal article
Journal
European journal of combinatorics
Date of publication
2012-04-02
Volume
33
Number
3
First page
302
Last page
325
DOI
https://doi.org/10.1016/j.ejc.2011.09.010 Open in new window
Repository
http://hdl.handle.net/2117/87102 Open in new window
Abstract
It is well-known that the triangulations of the disc with n + 2 vertices on its boundary are counted by the nth Catalan number C(n) = 1 n+1 (2n n ) . This paper deals with the generalisation of this problem to any compact surface S with boundaries. We obtain the asymptotic number of simplicial decompositions of the surface S with n vertices on its boundary. More generally, we determine the asymptotic number of dissections of S when the faces are d-gons with d belonging to a set of admissible deg...
Citation
Bernardi, O., Rue, J. Enumerating simplicial decompositions of surfaces with boundaries. "European journal of combinatorics", 02 Abril 2012, vol. 33, núm. 3, p. 302-325.
Group of research
GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics

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