Friezes for a pair of pants

Canakci, I.; Garcia Elsener, A.; Felikson, A.; Tumarkin, P.

Abstract

Frieze patterns are numerical arrangements that satisfy a local arithmetic rule. These arrangements are actively studied in connection to the theory of cluster algebras. In the setting of cluster algebras, the notion of a frieze pattern can be generalized, in particular to a frieze associated with a bordered marked surface endowed with a decorated hyperbolic metric. We study friezes associated with a pair of pants, interpreting entries of the frieze as λ-lengths of arcs connecting the marked points. We prove that all positive integral friezes over such surfaces are unitary, i.e. they arise from triangulations with all edges having unit λ-lengths.

Citation

Canakci, I., Garcia Elsener, A., Felikson, A., & Tumarkin, P. (2022). Friezes for a pair of pants. Séminaire lotharingien de combinatoire, 86B, Article 32

• Journal Article Type: Article
• Publication Date: 2022
• Deposit Date: Jul 7, 2022
• Publicly Available Date: Sep 8, 2022
• Journal: Séminaire Lotharingien de Combinatoire
• Electronic ISSN: 1286-4889
• Publisher: Fakultät für Mathematik, Universität Wien
• Peer Reviewed: Peer Reviewed
• Volume: 86B
• Article Number: 32
• Public URL: https://durham-repository.worktribe.com/output/1199777
• Publisher URL: https://www.emis.de/journals/SLC/index.html
• Related Public URLs: https://arxiv.org/abs/2111.13135