We generalize results of Calderbank, Hanlon and Robinson on the representation of the symmetric group on the homology of posets of partitions with restricted block size. Calderbank, Hanlon and Robinson consider the cases of block sizes that are congruent to 0 mod d and 1 mod d for fixed d . We derive a general formula for the representation of the symmetric group on the homology of posets of pa...

We will show that shellability, Cohen-Macaulayness and vertexde composability of a graded, planar poset P are all equivalent with the fact that P has the maximal possible number of edges. Also, for a such poset we will find an R−labelling with {1, 2} as the set of labels. Using this, we will obtain all essential linear inequalities for the flag h−vectors of shellable planar posets from [1]. AMS...

For every hypergraph on n vertices there is an associated subspace arrangement in R n called a hypergraph arrangement. We prove shellability for the intersection lattices of a large class of hypergraph arrangements. This class incorporates all the hypergraph arrangements which were previously shown to have shellable intersection lattices.

This is a direct continuation of Shellable Nonpure Complexes and Posets. I, which appeared in Transactions of the American Mathematical Society 348 (1996), 1299-1327. 8. Interval-generated lattices and dominance order In this section and the following one we will continue exemplifying the applicability of lexicographic shellability to nonpure posets. Let F = {I1, I2, . . . , In} be a family of ...

We introduce and study a class of simplicial complexes, the orphan complexes, associated to simple graphs whose family of (open or closed) vertex-neighborhoods are anti-Sperner. Under suitable restrictions, we show that orphan complexes of such graphs are always shellable and provide a characterization of graphs in terms of induced forbidden subgraphs contained in this restricted subfamily.

We give a case-free proof that the lattice of noncrossing partitions associated to any finite real reflection group is EL-shellable. Shellability of these lattices was open for the groups of type Dn and those of exceptional type and rank at least three.

We show that the stellar subdivisions of a simplex are extendably shellable. These polytopes appear as the facets of the dual of a hypersimplex. Using this fact, we calculate the simplicial and toric h-vector of the dual of a hypersimplex. Finally, we calculate the contribution of each shelling component to the toric h-vector.

Among shellable complexes a certain class is shown to have maximal modular homology, and these are the so-called saturated complexes. We show that certain conditions on the links of the complex imply saturation. We prove that Coxeter complexes and buildings are saturated. © 2002 Elsevier Science (USA)