Number of Triangulations of a Möbius Strip

Abstract

Consider a Möbius strip with $n$ chosen points on its edge. A triangulation is a maximal collection of arcs among these points and cuts the strip into triangles. In this paper, we proved the number of all triangulations that one can obtain from a Möbius strip with $n$ chosen points on its edge is given by $4^{n-1}+\left(\genfrac{}{}{0ex}{}{2n-2}{n-1}\right)$, then we made the connection with the number of clusters in the quasi-cluster algebra arising from the Möbius strip.

References in corpus (2)

• Cluster algebras in algebraic Lie theory
• Positivity for quasi-cluster algebras