Codismantlability and projective dimension of the Stanley-Reisner ring of special hypergraphs

TL;DR

This paper extends concepts of codismantlability and bouquets from graphs to hypergraphs, using these to analyze the projective dimension of Stanley-Reisner rings of certain hypergraphs.

Contribution

It introduces generalized notions of codismantlability and bouquets for hypergraphs and links these to the projective dimension of their Stanley-Reisner rings.

Findings

Some vertex decomposable hypergraphs are codismantlable.

New combinatorial invariants characterize projective dimension.

Extension of graph concepts to hypergraphs for algebraic analysis.

Abstract

In this paper firstly, we generalize the concept of codismantlable graphs to hypergraphs and show that some special vertex decomposable hypergraphs are codismantlable. Then we generalize the concept of bouquet in graphs to hypergraphs to extend some combinatorial invariants of graphs about disjointness of a set of bouquets. We use these invariants to characterize the projective dimension of Stanley-Reisner ring of special hypergraphs in some sense.