Abstract
We use the theory of lexicographic shellability to provide various examples
in which the rank of the homology of a Rees product of two partially ordered
sets enumerates some set of combinatorial objects, perhaps according to some
natural statistic on the set. Many of these examples generalize a result of J.
Jonsson, which says that the rank of the unique nontrivial homology group of
the Rees product of a truncated Boolean algebra of degree $n$ and a chain of
length $n-1$ is the number of derangements in $\S_n$.\
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