Number of Triangulations of a Möbius Strip
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 $4^{n-1}+\binom{2n-2}{n-1}$, then we made the connection with the number of clusters in the quasi-cluster algebra arising from the Möbius strip.
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