The Average Number of Non-Separating Edges in Catalan Triangulations of the Mőbius Band and the Cylinder
نویسندگان
چکیده
Let Σ be a surface whose boundary consists of a set of disjoint simple closed curves. A Catalan triangulation of Σ is a triangulation of Σ such that all vertices are on the boundary. An edge in a Catalan triangulation is called separating if the removal of its end vertices disconnects the triangulation. The number of Catalan triangulations of a disk is given by the well-known Catalan numbers. Catalan triangulations of the Mőbius band were counted recently by Edelman and Reiner. In this paper, we study the average number of separating edges in Catalan triangulations of the Mőbius band and the cylinder. The total number of Catalan triangulations of the cylinder is also given. Keywords1: Catalan triangulation, Mőbius Band, Cylinder, Enumeration, Separating edge. ∗Research supported by NSERCC 1991 Mathematics Subject Classification: 05C30
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