Plane Trees and H-Vectors of Shellable Cubical Complexes

Stanley first defined the generalized toric h-vector, a fundamental combinatorial invariant of polyhedral complexes (and more general objects). In the case where the complex is simplicial, this invariant can be computed by shelling, or taking apart the complex in a certain order. This paper shows how any shellable complex with cubical facets can be dealt with analogously. Based on a result of Shapiro the h-vector of any shellable cubical complex is formulated in terms of certain classes of plane trees.