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# Journal of Combinatorics

## Volume 3 (2012)

### Number 3

### Rees products and lexicographic shellability

Pages: 243 – 276

DOI: https://dx.doi.org/10.4310/JOC.2012.v3.n3.a1

#### Authors

#### 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 ${\mathfrak S}_n$.

Published 19 February 2013