8 citations · 12 across the 8 of their papers we have counts for
4 papers · 2 filters
Sequentially Cohen-Macaulay Edge Ideals
Christopher A. Francisco, Adam Van Tuyl
Let G be a simple undirected graph on n vertices, and let I(G) \subseteq R = k[x_1,...,x_n] denote its associated edge ideal. We show that all chordal graphs G are sequentially Coh…
Some families of componentwise linear monomial ideals
Christopher A. Francisco, Adam Van Tuyl
Let R=k[x_1,...,x_n] be a polynomial ring over a field k. Let J={j_1,...,j_t} be a subset of [n]={1,...,n}, and let m_J denote the ideal (x_{j_1},...,x_{j_t}) of R. Given subsets J…
New approaches to bounding the multiplicity of an ideal
Christopher A. Francisco
We use the theory of resolutions for a given Hilbert function to investigate the multiplicity conjectures of Huneke and Srinivasan and Herzog and Srinivasan. To prove the conjectur…
On the componentwise linearity and the minimal free resolution of a tetrahedral curve
Christopher A. Francisco, Juan C. Migliore, Uwe Nagel
A tetrahedral curve is an unmixed, usually non-reduced, one-dimensional subscheme of projective 3-space whose homogeneous ideal is the intersection of powers of the ideals of the s…