Matchings in hypergraphs and Castelnuovo-Mumford regularity

TL;DR

This paper extends combinatorial invariants like matching numbers to hypergraphs and explores their relationship with the algebraic regularity of Stanley-Reisner rings, providing new bounds for certain hypergraphs.

Contribution

It introduces generalized matching invariants for hypergraphs and establishes upper bounds for the regularity of associated Stanley-Reisner rings based on these invariants.

Findings

Generalized matching numbers for hypergraphs introduced

Upper bounds for Stanley-Reisner ring regularity established

Comparison of different matching invariants in hypergraph context

Abstract

In this paper, we introduce and generalize some combinatorial invariants of graphs such as matching number and induced matching number to hypergraphs. Then we compare them together and present some upper bounds for the regularity of Stanley-Reisner ring of $\Delta_{\mathcal{H}}$ for certain hypergraphs $\mathcal{H}$ in terms of the introduced matching numbers.