  We investigate possible parafermionic states in rapidly rotating ultracold
bosonic atomic gases at lowest Landau level filling factor nu=k/2. We study how
the system size and interactions act upon the overlap between the true ground
state and a candidate Read-Rezayi state. We also consider the quasihole states
which are expected to display non-Abelian statistics. We numerically evaluate
the degeneracy of these states and show agreement with a formula given by E.
Ardonne. We compute the overlaps between low-lying exact eigenstates and
quasihole candidate wavefunctions. We discuss the validity of the parafermion
description as a function of the filling factor.
