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Friezes for a pair of pants

Canakci, I. and Garcia Elsener, A. and Felikson, A. and Tumarkin, P. (2022) 'Friezes for a pair of pants.', Séminaire Lotharingien de Combinatoire, 86B .


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.

Item Type:Article
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Date accepted:No date available
Date deposited:08 September 2022
Date of first online publication:2022
Date first made open access:08 September 2022

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