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Friezes for a pair of pants

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

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I. Canakci

A. Garcia Elsener


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.

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
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