Our work, which makes an extensive use of both algebraic and combinatorial techniques, in
particular includes:(i) A characterization of the first half of a pure O-sequence, which yields …

Star configurations are certain unions of linear subspaces of projective space that have
been studied extensively. We develop a framework for studying a substantial generalization …

We introduce a construction on a flag complex that by means of modifying the associated
graph generates a new flag complex whose h-vector is the face vector of the original …

Geometric vertex decomposition and liaison are two frameworks that have been used to
produce similar results about similar families of algebraic varieties. In this paper, we …

The geometric vertex decomposability property for polynomial ideals is an ideal-theoretic
generalization of the vertex decomposability property for simplicial complexes. Indeed, a …

In this paper, we give a sufficient condition for a set G of polynomials to be a Gröbner basis
with respect to a given term-order for the ideal I that it generates. Our criterion depends on …

In this paper we study how prime filtrations and squarefree Stanley decompositions of
squarefree modules over the polynomial ring and over the exterior algebra behave with …

We introduce a new Macaulay2 package, SimplicialDecomposability, which works in
conjunction with the extant package SimplicialComplexes in order to compute a shelling …

Let $\mathbb {K} $ be a field and let $ S=\mathbb {K}[x_1,\dots, x_n] $ be the polynomial ring
in $ n $ variables over $\mathbb {K} $. Assume that $ I\subset S $ is a squarefree monomial …

We investigate Rees algebras and special fiber rings obtained by blowing up specialized
Ferrers ideals. This class of monomial ideals includes strongly stable monomial ideals …