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 ...

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...

We show that an ’almost strong Lefschetz’ property holds for the barycentric subdivision of a shellable complex. From this we conclude that for the barycentric subdivision of a CohenMacaulay complex, the h-vector is unimodal, peaks in its middle degree (one of them if the dimension of the complex is even), and that its g-vector is an M -sequence. In particular, the (combinatorial) g-conjecture ...

We give a complete enumeration of combinatorial 3-manifolds with 10 vertices: There are precisely 247882 triangulated 3-spheres with 10 vertices as well as 518 vertex-minimal triangulations of the sphere product S×S and 615 triangulations of the twisted sphere product S×S. All the 3-spheres with up to 10 vertices are shellable, but there are 29 vertexminimal non-shellable 3-balls with 9 vertices.