Using Edge-induced and Vertex-induced Subhypergraph Polynomials

TL;DR

This paper investigates the properties and reconstructibility of edge-induced and vertex-induced subhypergraph polynomials, establishing their relation and connections to algebraic invariants of hypergraphs.

Contribution

It introduces the relation between subhypergraph polynomials and proves their reconstructibility, linking them to algebraic invariants of hypergraphs.

Findings

Both polynomials are reconstructible from hypergraph data.

Established a relation between the polynomials and the Hilbert series of the Stanley-Reisner ring.

Connected subhypergraph polynomials to algebraic invariants of hypergraphs.

Abstract

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 $\mathcal H$.