The flag f-vectors of three-colored complexes are characterized. This also characterizes the flag h-vectors of balanced Cohen-Macaulay complexes of dimension two, as well as the flag h-vectors of balanced shellable complexes of dimension two.

The class of Strongly Signable partially ordered sets is introduced and studied. It is show that strong signability, reminiscent of Björner–Wachs’ recursive coatom orderability, provides a useful and broad sufficient condition for a poset to be dual CR and hence partitionable. The flag h-vectors of strongly signable posets are therefore non-negative. It is proved that recursively shellable pose...

The concept of shellability of complexes is generalized by deleting the requirement of purity (i.e., that all maximal faces have the same dimension). The usefulness of this level of generality was suggested by certain examples coming from the theory of subspace arrangements. We develop several of the basic properties of the concept of nonpure shellability. Doubly indexed f -vectors and h-vector...

The set of all permutations, ordered by pattern containment, forms a poset. This paper presents the first explicit major results on the topology of intervals in this poset. We show that almost all (open) intervals in this poset have a disconnected subinterval and are thus not shellable. Nevertheless, there seem to be large classes of intervals that are shellable and thus have the homotopy type ...

All dissections of a convex (mn + 2)-gons into (m + 2)-gons are facets of a simplicial complex. This complex is introduced by S. Fomin and A.V. Zelevinsky in [7]. We reprove the result of E. Tzanaki about shellability of such complex by finding a concrete shelling order. Also, we use this shelling order to find a combinatorial interpretation of h-vector and to describe the generating facets of ...

The notion of a partitionable simplicial complex is extended to that of a signable partially ordered set. It is shown in a unified way that face lattices of shellable polytopal complexes, polyhedral cone fans, and oriented matroid polytopes, are all signable. Each of these classes, which are believed to be mutually incomparable, strictly contains the class of convex polytopes. A general suffici...

The theory of complexes of directed trees was initiated by Kozlov to answer a question by Stanley, and later on, results from the theory were used by Babson and Kozlov in their proof of the Lovász conjecture. We develop the theory and prove that complexes on directed acyclic graphs are shellable. A related concept is that of independence complexes: construct a simplicial complex on the vertex s...