Subdivision and enumeration in balanced complexes (f-vector, stellar subdivision, h-vector, simplicial, polytope)
Katherine Eberhardt Magurn · 1985
The object of study is the affine space generated by the extended h-vectors of simplicial homology (d-l)-spheres which are balanced of a given type. The dimension of the space is computed by deriving a balanced version of the Dehn-Sommerville equations and exhibiting a set of balanced polytopes whose extended h-vectors span the space. These polytopes are obtained by balanced stellar subdivisions on the minimal balanced polytope of the given type. Balanced PL equivalence and balanced stellar equivalence are compared and related to PL and stellar equivalence as defined for unlabeled complexes. Minimal balanced stellar balls and spheres are defined and the question of what can be generated from them using balanced moves is examined.