Rees products and lexicographic shellability

Details Rees products and lexicographic shellability Rees products and lexicographic shellability

2012-03-05

arxiv.org/abs/1203.0922v1

Mathematics

Combinatorics

31 pages; 1 figure; part of this paper was originally part of the longer paper arXiv:0805.2416v1, which has been split into th

Scientific paper

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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