Abstract:

Major connection between combinatorics and geometry is due to polytopes. Polytopes are frequently used in the study of both theoretical and applied areas of mathematics. Much progress has been made in recent years in order to understand their combinatorial properties. Much of enumerative combinatorics of polytopes is captured in the f-vector. Equivalent information is carried by the h-vector in an elegant fashion. Simplicial polytope is the best understood class of polytopes. The study of face characterization of cubical complexes is getting attention nowadays because of the simplicity of its structural units. Adin identified the face characterization of cubical complex in terms of cubical h-vectors. Subdivisions of polytopes, on the other hand has been receiving extensive attention over the past few years. We are interested in presenting the characterization of barycentric subdivisions of cubical complexes using transformation of f-vector and h-vector of cubical complexes.