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.
|Full text:||(AM) Accepted Manuscript|
Download PDF (192Kb)
|Publisher Web site:||https://www.emis.de/journals/SLC/index.html|
|Date accepted:||No date available|
|Date deposited:||08 September 2022|
|Date of first online publication:||2022|
|Date first made open access:||08 September 2022|
Save or Share this output
|Look up in GoogleScholar|