8 papers
Edge ideals of gapfree graphs with matching number
Nursel Erey, Tài Huy Hà, Takayuki Hibi +2
We prove that if is a gapfree graph with matching number , then every power , , of its edge ideal has linear quotients, and hence a linear resolution. Our ap…
Symbolic powers and integral closures via extremal ideals
Trung Chau, Art Duval, Sara Faridi +3
This paper demonstrates that extremal ideals can be used to great effect to compute integral closures of powers and symbolic powers of square-free monomial ideals. We show that the…
Divisibility Relations and -Extremal ideals
Susan M. Cooper, Sabine El Khoury, Sara Faridi +3
A divisibility relation between the generators of a square-free monomial ideal formally encodes the situation when one generator divides the least common multiple of some other gen…
Realizing resolutions of powers of extremal ideals
Trung Chau, Art M. Duval, Sara Faridi +3
Extremal ideals are a class of square-free monomial ideals which dominate and determine many algebraic invariants of powers of all square-free monomial ideals. For example, the $r^…
Gapfree graphs and powers of edge ideals with linear quotients
Nursel Erey, Sara Faridi, Tài Huy Hà +3
Let be the edge ideal of a gapfree graph . An open conjecture of Nevo and Peeva states that has linear resolution for . We present a promising approach t…
Regular Edges, Matchings and Hilbert Series
Joseph Brennan, Susan Morey
When is the edge ideal of a graph , we use combinatorial properities, particularly Property on connectivity of neighbors of an edge, to classify when a binomial sum of v…
Scarf complexes of graphs and their powers
Sara Faridi, Tài Huy Hà, Takayuki Hibi +1
Every multigraded free resolution of a monomial ideal I contains the Scarf multidegrees of I. We say I has a Scarf resolution if the Scarf multidegrees are sufficient to describe a…
Hilbert Coefficients and Sally Modules: A Survey of Vasconcelos' Contributions
Jooyoun Hong, Susan Morey
This paper surveys and summarizes Wolmer Vasconcelos' results surrounding multiplicities, Hilbert coefficients, and their extensions. We particularly focus on Vasconcelos' results…