  Following the idea of the continuity approach in [D. L. Zhou, Phys. Rev.
Lett. 101, 180505 (2008)], we obtain the degrees of irreducible multi-party
correlations in two families of $n$-qutrit Greenberger-Horne-Zeilinger type
states. For the pure states in one of the families, the irreducible 2-party,
$n$-party and $(n-m)$-party ($0< m < n-2$) correlations are nonzero, which is
different from the $n$-qubit case. We also derive the correlation distributions
in the $n$-qutrit maximal slice state, which can be uniquely determined by its
$(n-1)$-qutrit reduced density matrices among pure states. It is proved that
there is no irreducible $n$-qutrit correlation in the maximal slice state. This
enlightens us to give a discussion about how to characterize the pure states
with irreducible $n$-party correlation in arbitrarily high-dimensional systems
by the way of the continuity approach.
