  We investigate a class of non-Abelian spin-singlet (NASS) quantum Hall
phases, proposed previously. The trial ground and quasihole excited states are
exact eigenstates of certain k+1-body interaction Hamiltonians. The k=1 cases
are the familiar Halperin Abelian spin-singlet states. We present closed-form
expressions for the many-body wave functions of the ground states, which for
k>1 were previously defined only in terms of correlators in specific conformal
field theories. The states contain clusters of k electrons, each cluster having
either all spins up, or all spins down. The ground states are non-degenerate,
while the quasihole excitations over these states show characteristic
degeneracies, which give rise to non-Abelian braid statistics. Using conformal
field theory methods, we derive counting rules that determine the degeneracies
in a spherical geometry. The results are checked against explicit numerical
diagonalization studies for small numbers of particles on the sphere.
