HYPERGRAPHS AND REGULARITY OF SQUARE-FREE MONOMIAL IDEALS
HYPERGRAPHS AND REGULARITY OF SQUARE-FREE MONOMIAL IDEALS
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 …