Rees products and lexicographic shellability
Combinatorics
2012-03-06 v1 Commutative Algebra
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 and a chain of length is the number of derangements in .\
Cite
@article{arxiv.1203.0922,
title = {Rees products and lexicographic shellability},
author = {Svante Linusson and John Shareshian and Michelle L. Wachs},
journal= {arXiv preprint arXiv:1203.0922},
year = {2012}
}
Comments
31 pages; 1 figure; part of this paper was originally part of the longer paper arXiv:0805.2416v1, which has been split into three papers