Download this article
 Download this article For screen
For printing
Recent Issues

Volume 17
Issue 2, 183–362
Issue 1, 1–182

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Author Index
Coming Soon
Other MSP Journals
Number of triangulations of a Möbius strip

Véronique Bazier-Matte, Ruiyan Huang and Hanyi Luo

Vol. 16 (2023), No. 4, 547–562

Consider a Möbius strip with n 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 n chosen points on its boundary is given by 4n1 + 2n2 n1 . We then connect our finding with the number of clusters in the quasi-cluster algebra arising from the Möbius strip.

quasi-cluster algebras
Mathematical Subject Classification
Primary: 13F60
Received: 12 September 2020
Revised: 29 July 2022
Accepted: 5 August 2022
Published: 31 October 2023

Communicated by Kenneth S. Berenhaut
Véronique Bazier-Matte
Département de Mathématiques et de Statistiques
Université Laval
Québec, QC
Ruiyan Huang
Yale University
New Haven, CT
United States
Hanyi Luo
Harvey Mudd College
Claremont, CA
United States