14 papers · 1 filter
Cellular resolutions of second powers of square-free monomial ideals with divisibility relations
Susan M. Cooper, Sabine El Khoury, Sara Faridi +3
Using divisibility relations between the generators of a square-free monomial ideal , we describe divisibility relations between the generators of the second power . We the…
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…
Simplicial Resolutions of the Quadratic Power of Monomial Ideals
Susan M. Cooper, Sara Faridi, Hasan Mahmood
Given any monomial ideal minimally generated by monomials, we define a simplicial complex that supports a resolution of . We also define a subco…
When are Morse resolutions polyhedral?
Louis Bu, Sara Faridi, Iresha Madduwe Hewalage +5
It is known that the chain complex of a simplex on vertices can be used to construct a free resolution of any ideal generated by monomials, and as a direct result, the Bett…
Cohen-Macaulay squares of edge ideals
Sara Faridi, Takayuki Hibi
Let be a finite graph and its edge ideal. We give a full description of the Stanley--Reisner complex of the polarization of , naturally introducing the tools of…
Artinian Gorenstein algebras with binomial Macaulay dual generator
Nasrin Altafi, Rodica Dinu, Sara Faridi +4
This paper initiates a systematic study for key properties of Artinian Gorenstein \(K\)-algebras having binomial Macaulay dual generators. In codimension 3, we demonstrate that all…
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…
Polarization and Gorenstein liaison
Sara Faridi, Patricia Klein, Jenna Rajchgot +1
A major open question in the theory of Gorenstein liaison is whether or not every arithmetically Cohen--Macaulay subscheme of can be G-linked to a complete intersect…
Counting lattice points that appear as algebraic invariants of Cameron-Walker graphs
Sara Faridi, Iresha Madduwe Hewalage
In 2021, Hibi et. al. studied lattice points in that appear as $(\depth R/I,\dim R/I)$ when is the edge ideal of a graph on vertices, and showed these points…
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…
Spherical complexes
Sara Faridi, Thiago Holleben
In this paper we define spherical complexes as simplicial complexes with the property that every subcomplex obtained by a sequence of links and deletions either has trivial homolog…
The Scarf complex and betti numbers of powers of extremal ideals
Sabine El Khoury, Sara Faridi, Liana Sega +1
This paper is concerned with finding bounds on betti numbers and describing combinatorially and topologically (minimal) free resolutions of powers of ideals generated by a fixed nu…