Using Edge-Induced and Vertex-Induced Subhypergraph Polynomials

Abstract

For a hypergraph 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 H and the edge-induced subhypergraph polynomial. We also consider reconstruction of some algebraic invariants of H.