We show that the poset of aB partitions of an nd-set with block size divisible by d is shellable. Using similar techniques, it also follows that various other examples of exponential structures cited by Stanley are also shellable. The method used involves the notion of recursive atom orderings introduced by Bjorner and Wachs. AMS (MOS) subject classifications (1984). Primary: 06AlO; secondary: ...

For every directed graph D we consider the complex of all directed subforests Δ(D). The investigation of these complexes was started by D. Kozlov. We generalize a result of Kozlov and prove that complexes of directed trees of complete multipartite graphs are shellable. We determine the h-vector of Δ(Km,n) and the homotopy type of Δ( −→ Kn1,n2,...,nk ).

In geometric, algebraic, and topological combinatorics, the unimodality of combinatorial generating polynomials is frequently studied. Unimodality follows when polynomial (real) stable, a property often deduced via theory interlacing polynomials. Many open questions on stability pertain to enumeration faces cell complexes. this paper, we relate shellability We first derive sufficient condition ...

This paper introduces two new decomposition techniques which are related to the classical notion of shellability of simplicial complexes, and uses the existence of these decompositions to deduce certain numerical properties for an associated enumerative invariant. First, we introduce the notion of M-shellability, which is a generalization to pure posets of the property of shellability of simpli...

We consider a q-analogue of abstract simplicial complexes, called q-complexes, and discuss the notion shellability for such complexes. It is shown that q-complexes formed by independent subspaces q-matroid are shellable. Further, we explicitly determine homology corresponding to uniform q-matroids. also outline some partial results concerning determination arbitrary shellable q-complexes.

We prove that the external activity complex Act<(M) of a matroid is shellable. In fact, we show that every linear extension of LasVergnas’s external/internal order <ext/int on M provides a shelling of Act<(M). We also show that every linear extension of LasVergnas’s internal order <int on M provides a shelling of the independence complex IN(M). As a corollary, Act<(M) and M have the same hvecto...

Let W be a Weyl group corresponding to the root system An−1 or Bn. We define a simplicial complex ∆mW in terms of polygon dissections for such a group and any positive integer m. For m = 1, ∆ W is isomorphic to the cluster complex corresponding to W , defined in [9]. We enumerate the faces of ∆ W and show that the entries of its h-vector are given by the generalized Narayana numbers N W (i), de...