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Number of
triangulations of a Möbius strip
Véronique Bazier-Matte, Ruiyan Huang and Hanyi Luo |
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Vol. 16 (2023), No. 4, 547–562
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Abstract |
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Consider a Möbius strip with chosen points on its boundary. A triangulation is a maximal collection of arcs among these points and cuts the strip into triangles and quasi-triangles. We prove that the number of all triangulations that one can obtain from a Möbius strip with chosen points on its boundary is given by . We then connect our finding with the number of clusters in the quasi-cluster algebra arising from the Möbius strip. |
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Keywords
quasi-cluster algebras
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Mathematical Subject Classification
Primary: 13F60
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Milestones
Received: 12 September 2020
Revised: 29 July 2022
Accepted: 5 August 2022
Published: 31 October 2023
Communicated by Kenneth S. Berenhaut
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Authors |
| Véronique Bazier-Matte | |
| Département de Mathématiques et de
Statistiques Université Laval Québec, QC Canada |
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| Ruiyan Huang | |
| Yale University New Haven, CT United States |
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| Hanyi Luo | |
| Harvey Mudd College Claremont, CA United States |
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| © 2023 MSP (Mathematical Sciences Publishers). |
