Using Edge-induced and Vertex-induced Subhypergraph Polynomials

For a hypergraph $\mathcal H$, we consider the edge-induced and vertex-induced subhypergraph polynomials and study their relation. We use this relation to prove that both polynomials are reconstructible, and to prove a theorem relating the Hilbert series of the Stanley-Reisner ring of the independent complex of $\mathcal H$ and the edge-induced subhypergraph polynomial. We also consider reconstruction of some algebraic invariants of $\mathcal H$.