Balanced subdivision and enumeration in balanced spheres (Q1095917)

We study here the affine space generated by the extended f-vectors of simplicial homology (d-1)-spheres which are balanced of a given type. This space is determined, and its dimension is computed, by deriving a balanced version of the Dehn-Sommerville equations and exhibiting a set of balanced polytopes whose extended f-vectors span it. To this end, a unique minimal complex of a given type is defined, along with a balanced version of stellar subdivision, and such a subdivision of a face in a minimal complex is realized as the boundary complex of a balanced polytope. For these complexes, we obtain an explicit computation of their extended h-vectors, and, implicitly, f-vectors.