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arXiv · 1211.4301

Hypergraphs and the Regularity of Square-free Monomial Ideals

Kuei-Nuan Lin·Jason McCullough
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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.

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Kuei-Nuan Lin, Jason McCullough. 2013-03-29. Hypergraphs and the Regularity of Square-free Monomial Ideals. https://arxiv.org/abs/1211.4301

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