Counting 1-vertex Triangulations Of Oriented Surfaces

Details Counting 1-vertex Triangulations Of Oriented Surfaces Counting 1-vertex Triangulations Of Oriented Surfaces

2001-10-02

arxiv.org/abs/math/0110025v1

Mathematics

Combinatorics

15 pages, 2 figures

Scientific paper

A {\em $1-$vertex triangulation} of an oriented compact surface $S$ of genus $g$ is an embedded graph $T\subset S$ with a unique vertex such that all connected components of $S\setminus T$ are triangles (adjacent to exactly 3 edges of $T$). This paper gives formulas enumerating such triangulations (up to equivalence) on an oriented surface of given genus. {\em Une triangulation \`a un sommet} d'une surface orient\'ee compacte $S$ de genre $g$ est un graphe $T\subset S$ qui a un unique sommet et dont toutes les faces (composantes connexes de $S\setminus T$) sont des triangles (incidentes \`a trois ar\^etes de $T$). Cet article donne des formules permettant d'\'enum\'erer ces triangulations.

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