English

Hypergraphs and the Regularity of Square-free Monomial Ideals

Commutative Algebra 2013-04-02 v2 Combinatorics

Abstract

We define a new combinatorial object, which we call a labeled hypergraph, uniquely associated to any square-free monomial ideal. We prove several upper bounds on the regularity of a square-free monomial ideal in terms of simple combinatorial properties of its labeled hypergraph. We also give specific formulas for the regularity of square-free monomial ideals with certain labeled hypergraphs. Furthermore, we prove results in the case of one-dimensional labeled hypergraphs.

Keywords

Cite

@article{arxiv.1211.4301,
  title  = {Hypergraphs and the Regularity of Square-free Monomial Ideals},
  author = {Kuei-Nuan Lin and Jason McCullough},
  journal= {arXiv preprint arXiv:1211.4301},
  year   = {2013}
}

Comments

14 pages (Updated references. Fixed minor typos.)

R2 v1 2026-06-21T22:40:29.158Z