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arXiv · 2111.13135

Friezes for a pair of pants

Ilke Canakci·Anna Felikson·Ana Garcia Elsener·Pavel Tumarkin
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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 lambda-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 lambda-lengths.

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Ilke Canakci, Anna Felikson, Ana Garcia Elsener, Pavel Tumarkin. 2021-11-25. Friezes for a pair of pants. https://arxiv.org/abs/2111.13135

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