Subdivisions of shellable complexes

In geometric, algebraic, and topological combinatorics, the unimodality of combinatorial generating polynomials is frequently studied. Unimodality follows when polynomial (real) stable, a property often deduced via theory interlacing polynomials. Many open questions on stability pertain to enumeration faces cell complexes. this paper, we relate shellability We first derive sufficient condition for h-polynomial subdivision shellable complex. To apply it, generalize notion reciprocal domains convex embeddings polytopes abstract use generalization define family stable shellings polytopal characterize cubical simplicial complexes, answer question Brenti Welker barycentric subdivisions well-known polytopes. also give positive solution problem Mohammadi edgewise end by relating line combinatorics hyperplane arrangements. pose related questions, answers which would resolve some long-standing problems while strengthening ties between