# Enumerating simplicial decompositions of surfaces with boundaries - Mathematics > Combinatorics

Enumerating simplicial decompositions of surfaces with boundaries - Mathematics > Combinatorics - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Abstract: It is well-known that the triangulations of the disc with $n+2$ vertices onits boundary are counted by the $n$th Catalan number $Cn=\frac{1}{n+1}{2n\choose n}$. This paper deals with the generalisation of this problem to anyarbitrary compact surface $S$ with boundaries. We obtain the asymptotic numberof simplicial decompositions of the surface $S$ with $n$ vertices on itsboundary. More generally, we determine the asymptotic number of dissections of$S$ when the faces are $\delta$-gons with $\delta$ belonging to a set ofadmissible degrees $\Delta\subseteq \{3,4,5, .\}$. We also give the limit lawsof certain parameters of such dissections.

Autor: Olivier Bernardi LM-Orsay, Juanjo Rué

Fuente: https://arxiv.org/