  Young's lattice $L(m,n)$ consists of partitions having $m$ parts of size at
most $n$, ordered by inclusion of the corresponding Ferrers diagrams. K. O'Hara
gave the first constructive proof of the unimodality of the Gaussian
polynomials by expressing the underlying ranked set of $L(m,n)$ as a disjoint
union of products of centered rank-unimodal subsets. We construct a finer
decomposition which is compatible with the partial order on Young's lattice, at
the cost of replacing the cartesian product with a more general poset
extension. As a corollary, we obtain an explicit chain decomposition which
exhibits the rank-unimodality of $L(m,n)$. Moreover, this set of chains is
closed under the natural rank-flipping involution given by taking complements
of Ferrers diagrams.
