%0 Generic %1 linusson2012products %A Linusson, Svante %A Shareshian, John %A Wachs, Michelle L. %D 2012 %K product rees %T Rees products and lexicographic shellability %U http://arxiv.org/abs/1203.0922 %X 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 $\S_n$.\

@misc{linusson2012products, 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 $\S_n$.\}, added-at = {2019-12-17T21:09:13.000+0100}, author = {Linusson, Svante and Shareshian, John and Wachs, Michelle L.}, biburl = {https://www.bibsonomy.org/bibtex/2ab9ea52bbc3d06744ab83270860731fa/tomhanika}, description = {Rees products and lexicographic shellability}, interhash = {46be903c07039af363975d9fa653e4dc}, intrahash = {ab9ea52bbc3d06744ab83270860731fa}, keywords = {product rees}, note = {cite arxiv:1203.0922Comment: 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}, timestamp = {2019-12-17T21:09:13.000+0100}, title = {Rees products and lexicographic shellability}, url = {http://arxiv.org/abs/1203.0922}, year = 2012 }