Several Convex-Ear Decompositions

Cubical Convex Ear Decompositions

We consider the problem of constructing a convex ear decomposition for a poset. The usual technique, introduced by Nyman and Swartz, starts with a CL-labeling and uses this to shell the ‘ears’ of the decomposition. We axiomatize the necessary conditions for this technique as a “CL-ced” or “EL-ced”. We find an EL-ced of the d-divisible partition lattice, and a closely related convex ear decompos...

Coloring Complexes and Arrangements

Steingrimsson’s coloring complex and Jonsson’s unipolar complex are interpreted in terms of hyperplane arrangements. This viewpoint leads to short proofs that all coloring complexes and a large class of unipolar complexes have convex ear decompositions. These convex ear decompositions impose strong new restrictions on the chromatic polynomials of all finite graphs.

Convex-Ear Decompositions and the Flag h-Vector

We prove a theorem allowing us to find convex-ear decompositions for rankselected subposets of posets that are unions of Boolean sublattices in a coherent fashion. We then apply this theorem to geometric lattices and face posets of shellable complexes, obtaining new inequalities for their h-vectors. Finally, we use the latter decomposition to give a new interpretation to inequalities satisfied ...

Schauder decompositions in locally convex spaces

Poset Convex-ear Decompositions and Applications to the Flag H-vector

Possibly the most fundamental combinatorial invariant associated to a finite simplicial complex is its f-vector, the integral sequence expressing the number of faces of the complex in each dimension. The h-vector of a complex is obtained by applying a simple invertible transformation to its f-vector, and thus the two contain the same information. Because some properties of the f-vector are easi...