Enumerating simplicial decompositions of surfaces with boundaries

Authors:
Olivier Bernardi;Juanjo Rué
Affiliations:
CNRS, Département de Mathématiques, Université Paris-Sud, 91405 Orsay, France;Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), 28049 Madrid, Spain
Venue:
European Journal of Combinatorics
Year:
2012

Citing 5
Cited 0

On an asymptotic method in enumeration

Journal of Combinatorial Theory Series A
The number of rooted maps on an orientable surface

Journal of Combinatorial Theory Series A
The number of degree restricted maps on general surfaces

Discrete Mathematics - Special issue on discrete mathematics in China
Analytic Combinatorics

Analytic Combinatorics
A Bijection for Rooted Maps on Orientable Surfaces

SIAM Journal on Discrete Mathematics

Quantified Score

Hi-index	0.00

Visualization

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)=1n+12nn. 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 degrees @D@?{3,4,5,...}. We also give the limit laws for certain parameters of such dissections.