Powers of the edge ideals and matchings in hypergraphs

TL;DR

This paper establishes combinatorial lower bounds for the regularity of powers of edge ideals in uniform hypergraphs, introduces hypergraph families that attain these bounds, and highlights differences from previous bounds.

Contribution

It provides new combinatorial lower bounds for regularity of hypergraph edge ideals and identifies hypergraph families where these bounds are tight.

Findings

New lower bounds for regularity of powers of hypergraph edge ideals

Identification of hypergraph families attaining these bounds

Significant differences from previously known bounds

Abstract

In this work, some combinatorial lower bound for regularity of powers of the edge ideal of a uniform hypergarph is gained. A family of hypergraphs whose regularity of edge ideal attains this bound and has a significant difference from the lower bounds heretofore obtained have also been introduced.