Kuei-Nuan Lin

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 of square-free monomial ideals with certain labeled hypergraphs. Furthermore, we prove results in the case of one-dimensional labeled hypergraphs.

Rees algebras of square-free monomial ideals

We study the defining equations of the Rees algebra of square-free monomial ideals in a polynomial ring over a field. We determine that when an ideal

Projective Dimension of String and Cycle Hypergraphs

I

Normal 0-1 Polytopes

is generated by

Rees algebras of diagonal ideals

n

Hypergraphs with high projective dimension and 1-dimensional hypergraphs

square-free monomials of the same degree then

Cohen–Macaulayness of Rees Algebras of Modules

I

Cohen-Macaulayness of Rees algebras of diagonal ideals

has relation type at most

Rees algebras of truncations of complete intersections

n-2

Edge ideals of oriented graphs.

as long as