This paper presents identities
on generating functions for multisectioned partitions of integers by developing in the
language of partitions some powerful and essentially combinatorial techniques from
the literature of principal differential ideals. D. Mead has stated in Vol. 42 of this
journal that one can obtain interesting combinatorial relations by constructing
different vector space bases for a subspace of a differential ring and using the fact
that the cardinality of all bases is the same. The results of the present paper are of
this nature.
