  We show the existence of a series of transforms that capture several
structures that underlie higher-dimensional partitions. These transforms lead
to a sequence of triangles whose entries are given combinatorial
interpretations as the number of particular types of skew Ferrers diagrams. The
end result of our analysis is the existence of a triangle, that we denote by F,
which implies that the data needed to compute the number of partitions of a
given positive integer is reduced by a factor of half. The number of spanning
rooted forests appears intriguingly in a family of entries in the triangle F.
Using modifications of an algorithm due to Bratley-McKay, we are able to
directly enumerate entries in some of the triangles. As a result, we have been
able to compute numbers of partitions of positive integers <= 25 in any
dimension.
