Séminaire Lotharingien de Combinatoire, 86B.32 (2022), 12 pp.
İlke Çanakçı, Anna Felikson, Ana Garcia-Elsener
and Pavel Tumarkin
Friezes for a Pair of Pants
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.
Received: November 25, 2021.
Accepted: March 4, 2022.
Final version: April 1, 2022.
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