  A quiver mutation loop is a sequence of mutations and vertex relabelings,
along which a quiver transforms back to the original form. For a given mutation
loop, we introduce a quantity called a partition q-series. The partition
q-series are invariant under pentagon moves. If the quivers are of Dynkin type
or square products thereof, they reproduce so-called parafermionic or
quasi-particle character formulas of certain modules associated with affine Lie
algebras. They enjoy nice modular properties as expected from the conformal
field theory point of view.
