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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