2012/03/05 by Svante Linusson, Linusson, Svante, John Shareshian +3
Mathematics · #05A30 #05E05 #05E45 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.CO #msc:05A30 #msc:05E05 #msc:05E45
paper · pdf · doi:10.48550/arxiv.1203.0922
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
arxiv created 2012/03/05 · arxiv updated 2012/03/06
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 §n.\