Contents Online
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