English

Number of Triangulations of a M\"obius Strip

Combinatorics 2023-11-08 v1

Abstract

Consider a M\"obius strip with nn 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 M\"obius strip with nn chosen points on its edge is given by 4n1+(2n2n1)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 M\"obius strip.

Keywords

Cite

@article{arxiv.2009.05785,
  title  = {Number of Triangulations of a M\"obius Strip},
  author = {Bazier-Matte Véronique and Huang Ruiyan and Luo Hanyi},
  journal= {arXiv preprint arXiv:2009.05785},
  year   = {2023}
}