Friezes for a pair of pants

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

Friezes for a pair of pants

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

Authors

I. Canakci

A. Garcia Elsener

Professor Anna Felikson anna.felikson@durham.ac.uk
Professor

Professor Pavel Tumarkin pavel.tumarkin@durham.ac.uk
Professor

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
Publisher	Fakultät für Mathematik, Universität Wien
Peer Reviewed	Peer Reviewed
Volume	86B
Article Number	32
Publisher URL	https://www.emis.de/journals/SLC/index.html
Related Public URLs	https://arxiv.org/abs/2111.13135