  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.
