## Rees products and lexicographical shellability

**
Svante Linusson, John Shareshian and Michelle Wachs**
**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 the symmetric group S_n.

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