Counting 1-vertex triangulations of oriented surfaces Original Research Article

A 1-vertex triangulation of an oriented compact surface S of genus g is an embedded graph T⊂S having only one vertex such that all the connected components of S⧹T are exactly adjacent to 3 edges of T (i.e. are triangles). This paper gives formulas for the number of such triangulations (up to equivalence) on an oriented surface of given genus.